First, remember who was speaking on behalf of whom
Rather than cherry picking scripture and wondering at semantic distinctions in English translations, it is helpful to read the surrounding passages for context and to be familiar with the Gospels.
Chapter 15 of Acts informs us that the letter being quoted in 15:28 was the product from a council of the (Apostolic) leaders of the Church in Jerusalem. (See details in Acts 15: 1-22). James and Peter weighed in on the decision regarding what Gentiles should do in living their lives as followers of Christ and relaxation of some Mosaic laws. The NAB posted at the Vatican website includes these two1 notes note for the chapter:
[1-35] The Jerusalem "Council2" marks the official rejection of the rigid view that Gentile converts were obliged to observe the Mosaic law completely.
[7-11] Paul's refusal to impose the Mosaic law on the Gentile Christians is supported by Peter on the ground that within his own experience God bestowed the holy Spirit upon Cornelius and his household without preconditions concerning the adoption of the Mosaic law (see Acts 10:44-47).
From whence the authority of James and Peter?
Jesus told his followers about the Holy Spirit coming to them "from above."
(John 3:5 Jesus answered, "Amen, amen, I say to you, no one can enter the
kingdom of God without being born of water and Spirit. 6 What is
born of flesh is flesh and what is born of spirit is spirit. 7 Do
not be amazed that I told you, 'You must be born from above.' 8 The
wind blows where it wills, and you can hear the sound it makes, but
you do not know where it comes from or where it goes; so it is with
everyone who is born of the Spirit."
And it came to pass. (Acts 2)
1 When the time for Pentecost was fulfilled, they were all in one
place together. 2 And suddenly there came from the sky a noise like a
strong driving wind, and it filled the entire house in which they
were. 3 Then there appeared to them tongues as of fire, 3 which
parted and came to rest on each one of them. 4 And they were all
filled with the holy Spirit ... {snip}
Jesus promised the Apostles that the Holy Spirit would help them; Jesus promised an Advocate in John 16:
7 But I tell you the truth, it is better for you that I go. For if I
do not go, the Advocate will not come to you. But if I go, I will send
him to you. {snip} 12 "I have much more to tell you, but you cannot
bear it now. 13 But when he comes, the Spirit of truth, he will guide
you to all truth. He will not speak on his own, but he will speak what
he hears, and will declare to you the things that are coming. 14 He
will glorify me, because he will take from what is mine and declare it
to you. 15 Everything that the Father has is mine; for this reason I
told you that he will take from what is mine and declare it to you.{Italics added}
With the above mind, the letter indicating the ruling from the Apostolic council in Jerusalem is delivered by Silas and Judas. The authors of the letter humbly present that the primary authority for this decision is the Holy Spirit -- the message is that the council received guidance from their Advocate in coming to this decision.
From the NAB, ACTS 15:
24 Since we have heard that some of our number (who went out) without
any mandate from us have upset you with their teachings and disturbed
your peace of mind, 25 we have with one accord decided to choose
representatives and to send them to you along with our beloved
Barnabas and Paul, 26 who have dedicated their lives to the name of
our Lord Jesus Christ. 27 So we are sending Judas and Silas who will
also convey this same message by word of mouth: 28 'It is the
decision of the holy Spirit and of us not to place on you any burden
beyond these necessities, 29 namely, to abstain from meat sacrificed
to idols, from blood, from meats of strangled animals, and from
unlawful marriage. If you keep free of these, you will be doing what
is right. Farewell.'" 30 And so they were sent on their journey.
Upon their arrival in Antioch they called the assembly together and
delivered the letter. 31 When the people read it, they were
delighted with the exhortation.
This pattern has been replicated over the years and anchors the Catholic Church's belief that ecumenical councils are guided and aided by the Holy Spirit. (The Advocate, also called the Paraclete) For example, from the council of Florence:
For the praise of almighty God, the exaltation of the catholic faith
and the peace, tranquility and unity of the whole Christian people.
This holy universal synod, through the grace of God authorized by the
most blessed lord pope Eugenius IV, legitimately assembled in the holy
Spirit in this city of Ferrara, represents the universal church.
From the commentary on this verse in the Douay Rheims Bible (thanks to @Geremia for the inspiration and the link)
Secondly we note, that the holy Councils lawfully kept for
determination, or clearing of doubts, or condemning of errors and
Heresies, or appeasing of Schisms and troubles, or reformation of
life, and such like important matters, have ever the assistance of
God's Spirit, and therefore cannot err in their sentences and
determination concerning the same, because the Holy Ghost cannot err,
from whom (as you see here) jointly with the Council the resolution
proceedeth.
The Catechism quotes St Cyril of Alexandria's point on how the Church fulfills its mission with the Holy Spirit.
CCC 738 Thus the Church's mission is not an addition to that of
Christ and the Holy Spirit, but is its sacrament: in her whole being
and in all her members, the Church is sent to announce, bear witness,
make present, and spread the mystery of the communion of the Holy
Trinity ...
All of us who have received one and the same Spirit, that is, the Holy
Spirit, are in a sense blended together with one another and with God.
For if Christ, together with the Father's and his own Spirit, comes to
dwell in each of us, though we are many, still the Spirit is one and
undivided. He binds together the spirits of each and every one of us,
. . . and makes all appear as one in him. For just as the power of
Christ's sacred flesh unites those in whom it dwells into one body, I
think that in the same way the one and undivided Spirit of God, who
dwells in all, leads all into spiritual unity. ~ St. Cyril of
Alexandria, In Jo. ev., 11,11: PG 74, 561.
Summary
The Apostles, the original the Disciples of Christ, were humble enough to acknowledge that they as Church -- Jesus' agents for spreading the Gospel -- needed the Holy Spirit (who Jesus promised would come to them) to help them in their mission. The opening salutation in that letter is both a humble admission that they had help and guidance in coming to their decision, and a reminder that it carries legitimate apostolic authority thanks to that guidance.
1 Notes on chapter 15 of ACTS (New American Bible) are used since that translation of the Bible has earned both Impramatur and nihil obstat notations.
2 One last note from the NAB:[13-35] Some scholars think that this apostolic decree suggested by James, the immediate leader of the Jerusalem community, derives from another historical occasion than the meeting in question. This seems to be the case if the meeting is the same as the one related in ⇒ Gal 2:1-10. {snip} See the full text at the linked site.