It seems like this is at least slightly backwards in reasoning. I think it has less to do with something sounding more precise than it does with the fact that,

It seems like this is at least slightly backwards in reasoning. I think it has less to do with something sounding more precise than it does with the fact that, in the real world, actual costs are only rarely a round number. As such, if there's a psychological association of non-round numbers sounding more precise, it's because non-round numbers are actually much more common. This means if you provide a round number bid, you are in reality more likely to have given a value that is incorrect.