No, that is not the issue. Under ‘first to invent’ the proof would have had to be provided that that was the case. In general terms, the same level of proof applies to show that the invention was not novel at the time of filing by a third party.
No one can obtain a valid patent under ‘first to file’ for something that was previously disclosed by public use or publication (other than in the 1 year grace period provided to the original inventor - 35 U.S.C. 102(b)).
Which is why intellectual property publication has become a big business.