After much more spelunking, it seems to be that:

1) The author of a status I replied to deleted the original status.
2) Instead of giving me back my status with its original in_reply_to_id, Mastodon rewrites history to make it appear as if I I'm just talking to myself. 😠

I was only able to verify this because I have my own backup of my mastodon history, which Mastodon can not rewrite.