You're possibly right with the scenario you paint but in reality no one knows the true situation. We could have offered 35 and we still would have got the bullshit of "well, we have to sign a replacement before we can let him go". That would given another club plenty of time to come in if they wanted to derail our transfer.
However, it all depends on what Sanchez wants. Does he want to join Pep and City and share in the success that we seem to be on the verge of attaining or does he want to put money first and risk the success which may or may not come with United. Decisions, decisions.