I know at least two situations where people have bid for their own players that haven't been discussed.
Once was me, I listed a player (ok it was late at night) and I left a "0" out. Ha ha. I did want to sell but I didn't want to sell him for $3,000 so I bid it to what I wanted as the real starting price. Mind you I did this within two minutes of the initial listing and he sold anyway.
The other time was a friend of mine who had just started playing. I was looking at the TL for guys to buy for my team, Aussie players, then I saw this guy ...and it was my friends. I sent him a message saying something like, "Why are you selling that guy, he is great?" There had been some bids already so he had to raise the bid and bought his own player back.
I think these are legitimate reasons to allow people to bid on their own players.