It's the former.
There's surprisingly little difference between real memories and imagined ones - namely the belief that it's not just imagined. Apply confirmation bias to that and you have a way of planting false memories.
I sometimes give "false memory placebos" where I use the same techniques to give false memories of having hypnotized them for some effect, which then happens because they expect it to. That wouldn't work if they didn't alieve it was real.
Only about half of the people being surveyed claimed to remember the false events, so clearly the procedure fails to produce false memories in a large proportion of those surveyed. Just because memories can be faked does not necessarily mean that all or even most of those claiming to remember the events have really produced false memories.
Although I have not done so on surveys, I can certainly attest that I've claimed to remember things that I didn't remember at all; most often I've done it to avoid embarrassing other people.
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.