If that's the case they should be better at identifying the fake event after they were told that one is fake.
For a bit, I thought that this seemed to set a floor on the number of respondents who must really be producing memories of the fake event (although significantly more people who claimed to remember the fake event picked it out as fake than would be predicted by chance if they had no way of distinguishing between them,) but it occurs to me that if the respondents were lying about remembering multiple events in the survey, then it doesn't seem that the survey would be able to distinguish between respondents who picked the wrong event as fake because they had...
Another one for the memory-is-really-unreliable file. Some researchers at UC Irvine (one of them is Elizabeth Loftus, whose name I've seen attached to other fake-memory studies) asked about 5000 subjects about their recollection of four political events. One of the political events never actually happened. About half the subjects said they remembered the fake event. Subjects were more likely to pseudo-remember events congruent with their political preferences (e.g., Bush or Obama doing something embarrassing).
Link to papers.ssrn.com (paper is freely downloadable).
The subjects were recruited from the readership of Slate, which unsurprisingly means they aren't a very representative sample of the US population (never mind the rest of the world). In particular, about 5% identified as conservative and about 60% as progressive.
Each real event was remembered by 90-98% of subjects. Self-identified conservatives remembered the real events a little less well. Self-identified progressives were much more likely to "remember" a fake event in which G W Bush took a vacation in Texas while Hurricane Katrina was devastating New Orleans. Self-identified conservatives were somewhat more likely to "remember" a fake event in which Barack Obama shook the hand of Mahmoud Ahmedinejad.
About half of the subjects who "remembered" fake events were unable to identify the fake event correctly when they were told that one of the events in the study was fake.