I don't think I've ever cared that someone passed me while I was training solo... I've never intentionally pushed harder to try and pass someone either. If it happens, it happens. It's not a race.
Although on my Sunday ride, I did have the pleasure of passing a group of guys twice. I caught up and passed them climbing a hill. I took it easy on the descent and they blew right by me. We hit the next hill and they practically came to a stop... I couldn't help but pass them again.