Well, the procedure we went through is, theoretically, the way it should be. But, your previous experience with a similar fault should protect you from the wrath of your boss and some understanding from me. Also, doubtless you would have recorded the details of your previous fault and you might have enquired to the cause after the investigation and wheel change. If that small cut was deemed to be the only cause (no binding brake, excessive wear, or another unseen cut on the underside of the tyre that was on the ground) I would expect the IPT and manufacturer to have already reviewed the acceptable limits. Of course, your previous event could have ocurred yesterday, so the investigation has hardly started. So, in that circumstance I, the Eng WO, and your boss, should be less draconian. The jet would remain on the programme.
However, your specific example is not at all realistic. If the book states that a small cut in a tyre is acceptable, it will be because the manufacturer has provided that assurance. Its not the RAF engineers that have made the decision unilaterally. So, in your example you are suggesting that manufacturers limits are not acceptable. I don't believe that you really mean that.
I'm comfortable that when the ground crew can make a clear "safe or nor not safe" decision (based on quality information), that we can trust them do it. If its safe, its acceptable. When they are faced with a grey area, their instinct is "not safe" and the jet is grounded until further information is received. I'm more than happy with this principle.
I've lost count of the number of times the types I've been associated with have been fleet-grounded over a weekend until the manaufacturer comes to work on Monday morning (you know what I mean) to give advice.
I remain convinced that you and I basically agree.