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.
It could be that Sancho rejected Chelsea's offer because he figured out he would have less playing time at Chelsea. It seems Sancho was looking for a club where he would be guaranteed a first-team match; that's why he accepted Juventus's offer. If Juventus finalizes the Sancho deal with Manchester United, Sancho will be certain of a first-team match because Juventus doesn't have enough squad depth that could make Sancho become a substitute player.