Micky
First off, it's one thing to self report that you do something wrong - yes, that needs to be encouraged. But that's not the case here.
But what really gets my attention is not that a mechanic forgot to do something - that happens - that's why we have inspectors. But how does an inspector inspect the job without recognizing it wasn't done? That makes me think that he didn't check, and if that was the case, it's pretty unlikely this was the very first time he signed off as checking a job when he hadn't in fact done that.
For an inspector - yes, that should get you sacked because it demonstrates a lack of integrity. It can also get people killed.