Well I just don't agree with that nor do I think it's common sense. It's standard thinking which is warped by the save stat but it's not common sense.
First I don't think he should come in every time we have a 4 run lead. In special circumstances it makes sense though. A 4 run lead vs the most potent offense in baseball's middle of the order is not your typical 4 run lead. Getting the final 3 outs in that situation would be harder than getting 3 outs against the bottom of the Twins lineup with a 3 run lead yet Osuna would be expected to get the ball in the latter situation because of a ******** stat called the save. On top of it these games against the Red Sox are extra important seeing as it likely comes down to us and them for who wins the division.
The Save is pretty much a ******** stat that somehow has completely hijacked the way managers and fans think the 9th inning should be managed. I think it should be ignored when making bullpen decisions.
EDIT: That said I do think that what you said makes sense. Grilli kind of scares me in a situation like that right now but putting in a Chavez or Floyd with a 4 run lead then going to Osuna if necessary and it's not like I would be blasting Gibbons for doing it. I'm just defending a bullpen move by Gibbons that isn't by the book but isn't necessarily wrong either.