I read the following comment on the secular internet in relation to the closing paragraphs of DN 2, where a King or layperson made an admission of a moral transgression/sin to the Buddha:
Yes that confession is especially by and to monks -- "the discipline" as you quoted it is the Vinaya.
Does the Pali word "vinaya" in the suttas always refer to the Vinaya Piṭaka, i.e., the Pāṭimokkha rules made exclusively for monks & nuns?
In DN 2 I doubt that the Buddha was referring to the Pāṭimokkha rules -- he was addressing a king (not a monk), and the king confesses taking the life of his father (which isn't, you know, one of Pāṭimokkha rules).
The PTS Dictionary gives other more general definitions, e.g.
norm of conduct, ethics, morality, good behaviour
... of which the "monastic discipline" or "canon law" is what I'd call a subtype of the more general class.
But the Vinaya does formulate confession, and experience with it I hope might acclimatize a monk to properly hearing an confession -- e.g. without "the destruction" which the OP feared would arise "if I told people close to me" -- especially a suitable confession i.e. as identified in that sentence of DN 2:
For it is growth in the training of the Noble One to recognize a mistake for what it is, deal with it properly, and commit to restraint in the future.
DN 2 contains the term "ariyassa vinaye", translated as "training of the Noble One". This term is also found, for example, in the Brāhmaṇapaccorohaṇī Sutta, another sutta addressed to a layperson. The sutta says:
But Master Gotama, how is the ceremony of descent observed in the training of the Noble One (ariyassa vinaye)? Master Gotama, please teach me this.”
“Well then, brahmin, listen and pay close attention, I will speak.”
“Yes sir,” Jāṇussoṇi replied. The Buddha said this:
“It’s when a noble disciple reflects: ‘Killing living creatures has a bad result in the present life and in lives to come.’ Reflecting like this, they give up killing living creatures, they descend from killing living creatures.
… ‘Stealing has a bad result in the present life and in lives to come.’ Reflecting like this, they give up stealing, they descend from stealing.
… ‘Sexual misconduct (kāmesumicchācārassa) has a bad result in the present life and in lives to come.’ Reflecting like this, they give up sexual misconduct, they descend from sexual misconduct.
‘Lying has a bad result in the present life and in lives to come.’ Reflecting like this, they give up lying, they descend from lying.
… ‘Divisive speech has a bad result in the present life and in lives to come.’ Reflecting like this, they give up divisive speech, they descend from divisive speech.
… ‘Harsh speech has a bad result in the present life and in lives to come.’ Reflecting like this, they give up harsh speech, they descend from harsh speech.
… ‘Talking nonsense has a bad result in the present life and in lives to come.’ Reflecting like this, they give up talking nonsense, they descend from talking nonsense.
… ‘Covetousness has a bad result in the present life and in lives to come.’ Reflecting like this, they give up covetousness, they descend from covetousness.
… ‘Ill will has a bad result in the present life and in lives to come.’ Reflecting like this, they give up ill will, they descend from ill will.
‘Wrong view has a bad result in the present life and in lives to come.’ Reflecting like this, they give up wrong view, they descend from wrong view. This is the ceremony of descent in the training of the Noble One.”
“The ceremony of descent observed by the brahmins is quite different from that observed in the training of the Noble One. And, Master Gotama, the ceremony of descent observed by the brahmins is not worth a sixteenth part of the ceremony of descent observed in the training of the Noble One. Excellent, Master Gotama, excellent! … From this day forth, may Master Gotama remember me as a lay follower who has gone for refuge for life.”
Obviously, the above is a standard teaching for laypeople, as found in many suttas, such as AN 10.176. For example, the term sexual misconduct (kāmesumicchācārassa) generally pertains to laypeople because for monks the relevent term is "abrahmacariyā".
In summary, it appears clear the term "ariyassa vinaye" as used in the suttas does not pertain exclusively to what today is known as the Bhikkhu Vinaya. It appears the secular blogger on the internet was wrong.