You shouldn't blame Sancho for refusing to accept Chelsea's offer because he thought he was going to get a better offer from another club, but that didn't happen because few clubs were only interested in signing him from Manchester United. I even heard the offer Sancho accepted from Juventus is even below what Chelsea offered him. Juventus and Manchester United have already agreed on a transfer fee for Sancho, and I don't think Inter Milan can hijack the deal because they need to agree on personal terms with Sancho first before they can submit a bid to Manchester United.
Maybe Sancho was not only motivated by the contract amount but also by whether he would get a place in the starting lineup or not. I think he has a much better chance of playing in Juventus than in Chelsea, where he would most likely become a player who often sits on the bench. I don't think Juventus is capable of getting a very big benefit from this transfer, but in recent seasons they have focused on such average transfers.