You may want to make a link to this post. There were a few different descriptions of why that problem (a very similar one) didn't work, and the one I pinpointed as "the pointer problem" is more or less that same as the one you pinpointed.

The flaw here is that we conditioned on person x existing, but person x only became of interest after we saw that they existed (peeked at the data).

Perhaps we could call the error a "pre-selection bias"?

(In a separate daughter comment, I'll summarize the anthropic problem described in the other post, emphasizing the similarity of the problems and the solutions. )