Well, we can assume that Neal would have wanted to find out everything there was to know about his hero father, maybe even brag about him a little and so on. He would have started researching and everything could have blown up into his face. Additionally, the case of Neal's father might have been a high profile one, so chances are that someone would have recognized the similarities in looks, etc... and perhaps there is another reason why Ellen didn't think it wise for Neal to pursue a career as a cop, a reason she just didn't tell Neal (which is also quite likely).