Using a random number generator is a very sensible and probably relatively common way for humans with a computer to pick "any" year, so I think that doing so is providing honest data, not fake data.

Where did the question ask us for a "random" number? "Some humans pick future years from underdetermined distributions by asking the most convenient RNG" is no more "fake" than, say, "Some humans pick future years from underdetermined distributions by recalling a fun sci-fi show".

Now that I've explained why lavalamp shouldn't feel guilty for asking his computer and I shouldn't feel guilty for asking pop culture: is it odd that I do feel guilty for picking something in this millenium? I know that a uniform distribution over Z+ doesn't exist, but it still feels like I ought to have at least added a digit or two.

Why would you do that? If you know this is set up to detect patterns in how humans pick random numbers, isn't specifically entering a data point in order to thwart that sort of like providing fake data on a survey to mess with the results?

It's like providing fake data on a survey intended to detect patterns in what fake data people will produce.

It was the most obvious way to avoid the anchoring effect? I kinda figured the OP was going to give the survey to multiple audiences and see if LW had a smaller anchoring effect.