In First Contact, Worf had knowledge of events happening at Deep Space Nine after Picard entered the Nexus - just the fact that he was at DS9 wouldn't be known to Picard. We can corroborate things he says against events on DS9.
In both Insurrection and Nemesis, multiple characters including Picard knew about the Dominion War in detail (some of which can be corroborated in DS9), but as Generations is stardated between The Jem'hadar and The Search, the only thing Picard would have known of the Dominion was that first contact had gone badly.
If Picard were still in the Nexus, we should be unable to corroborate outside events between later films and DS9.
There's also some two-way corroboration, as events in Generations are corroborated in both DS9 and Voyager. Worf, Barclay, and Riker were all on the Enterprise when it crashed, and we see that the Nexus does not sweep over their location when it picks up Soran and Picard. Had Picard stayed in the Nexus, they would have died in the supernova. However, Worf is transferred to DS9 (where he confirms that the Enterprise was destroyed), Barclay to Jupiter Station, and Riker is... somewhere when Q transports him briefly to Voyager. All three are seen in contexts outside of Picard's hypothetical fantasy, corroborating that they did survive. Therefore, Picard and Kirk's escape is confirmed.