I don't think they are very coddled. If a Fish's nature makes people pull their punches I think that is fair game. On another note the show is not outright sadism. I think Fish get challenged in proportion to what they can take for the most part. You can say Twins were never dogpiled nor a target for the kind of relentless harassment that would cause them to walk, but Twins are not the only Fish who avoided dogpiling. Fish who got lengthy bouts of either dogpiling or relentless harassment like JD and Bashir court that to some degree as well, when I don't think Twins really do.
I think the coddled accusation comes from Twins showing exploitable weakness that would be easy to needle them with that nobody capitalized on. Then people look at JD walking as an example for how Fish should be handled, its just that Twins walking like that would not be very funny and just kind of sad.