They are strange, and they're too convenient to accept because we all want to believe they're true - on a personal level I want last month's worst flu/cough of my life to be my infection, on a national scale, we want to think that lots of us have already has it, because all the models will then look a lot better in terms of the curves and where we are now. Unfortunately none of the testing data really backs it up, at the moment it's more of a "wouldn't it be nice" than something with an evidence base behind it.
That said, there are now some "strong, circumstantial" stories of earlier infections, like this one
https://www.telegraph.co.uk/global-...-sussex-family-may-have-infected-coronavirus/ that suggests at least one Brit had it back in mid-January (a month before the first tested positive case) and that he brought it back from a skiing trip in Austria and gave it to his family.
Only cases that ended up in hospital would have been noticed at all, and even there, an individual "odd" pneumonia particularly in an elderly patient wouldn't really be noticed at that time. When we get the antibody test we might actually start to understand the true story, and the history better.