The verb 「なる」, which is a key verb in the language, always describes a change of state as in:
・A turns into B.
・A becomes more/less (adjective).
・Situation A changes to situation B.
「情報{じょうほう}の真偽{しんぎ}を確{たし}かめるまで帰{かえ}れなくなった。」
This sentence talks about a (fairly recent) change of state as below:
Old state: One was free to leave or was about to leave.
Something happens that changes all that. ← Perhaps a new piece of information has come in.
Present state: One cannot leave until the authenticity of the information has been verified.
Old state (帰れた)⇒⇒ New state (帰れなくなった)
「帰れなくなった」=「帰れる」+「ない」+「なる」 in the past tense
Thus your first sentence means something along the lines of:
"It has (just) become impossible for me/us to leave until the authenticity of the information has been verified."
Your second sentence:
「情報の真偽を確かめるまで帰れない。」
says nothing about a change of state (like your first sentence does). It just means:
"One cannot leave until the authenticity of the information has been verified."