Contrary to what people may think, the bank don't own the house - the owners do. There may be a loan secured on the house, but the mortgage company can only order the house to be sold to recover their money if the owners don't keep to their side of the loan agreement.
I believe (although I may be wrong), that even if the bank did order the sale of the house owing to a big default on the mortgage agreement, they would still need to offer it on the open market and couldn't just choose their preferred buyer without doing this.
In fact, I think it would still be the owner in charge of the sale and able to choose their preferred buyer (as long as their offer was serious and sufficient to settle the loan) - it just wouldn't be an option for them not to put it up for sale.
If mortgage lenders could sell your house to anybody else on a whim, what would be the benefit in buying with a mortgage over renting? At least, when renting, you only have to commit to paying for 6/12 months and aren't responsible for the repairs yourself.
I'm yet another who is baffled as to why OP didn't strike with an unbeatably high offer when the house was on the market, though.