I think the Shat probably legitimately regretted hurting Wil, because, as was stated above...he didn't really mean to hurt him. I betcha Gene didn't tell him to apologize, probably just told him how bad Wil took it.
I don't know that I'd go that far. Knowing the type, and having been an unintentionally insensitive jerk a time or two, I think it more likely that Shatner just would not have understood how Wil took offense at his (lame attempt at) humor. The problem and the correction probably had to be explained to him in detail. Even then he probably wouldn't have totally understood the need to do so, perhaps not for many years, because a person like Wil would be as alien to him as IRL green women.