Neil did everything he could to stall Castellano while the boss wanted to hear A: The Ruggerio Tapes, and B: To Kill Gotti. When Neil died, Gotti and his crew would have rightfully be put into the ground. So they acted, but there is no way Neil would have touched Gotti - dont you think that Castellano had asked him to do so before? He'd wanted to kill Gotti long before.
In retrospect, accepting John into his family in 1977 was possibly the worst decision he ever made.