There are several rhetorical terms describing cases where someone calls attention to something under the pretense of not talking about it or claiming that it shouldn't be talked about, thereby indirectly calling attention to it): apophasis, paralipsis, preterition (amongst others).
Oftentimes, apophasis or paralipsis operates by implying that the audience already knows about the information that the speaker is "refusing" to bring up or, if they don't know about it, that it's because the information isn't important or relevant to the discussion at hand - thereby playing on irony in that the information indirectly mentioned is actually directly relevant to what the speaker wants the audience to consider.
What would be a rhetorical device for the reverse? When someone directly calls attention to something by reporting information that doesn't pertain to the issue at hand, under the pretense that they are best able to provide that information because the audience truly does not have access to it?
An example, from U.S. Senator Joseph McCarthy's 1950 "Enemies from Within" speech:
I have here in my hand a list of 205 ... a list of names that were made known to the Secretary of State as being members of the Communist Party and who nevertheless are still working and shaping policy in the State Department.
While McCarthy's claim of having exclusive knowledge about known Communists within the State Department was false (or at least misleading, depending on the account), he was able to use that information to pivot a speech meant to commemorate the 141st birthday of Abraham Lincoln into a proclamation that the U.S. government had been infiltrated by Communists, thus setting off the Red Scare.
It might be too easy to resolve that this is simply a case of lying or "bullshit". The information may be false, but the strategy I'm looking to identify extends to the purpose behind using the information.
Unlike apophasis, where a speaker can intentionally draw attention to something by claiming the pretense of "not talking about it", the case here shows how a speaker can report dubious information that hasn't been "talked about" prior to the speaker bringing it up. However, since the source is implied as being reliable (but inaccessible to the audience at that moment), the speaker is then able to build the rest of their argument on the presupposition that they are basing it on legitimate claims.