How do you rule?

[nzumpire]

R1 on 1st, running on the pitch. B2 hits a low line drive to F6, who catches the ball. F6 then throws to F3, attempting to catch R1 off base before he can return to tag-up after the catch. R1 attempts to return to 1st but is obstructed by F4.
The ball reaches F3, who touches 1st and legally appeals before R1 can recover and return to the base. The umpire considers R1 would not have returned in time, even had the obstruction not occurred, so calls R1 out.
The offensive team coach then insists that the out should be overturned, claiming that no runner can be called out between the bases where he was obstructed.