Coaching only matters if it is documented. I have a problem child on my team who was transferred to me with no write ups at all. No one bothered to tell me they were a problem case till it was too late, and then when the truth came out and I went to see how many coachings the TM had on file I found none. In six months of problems before this TM came to me, no one bothered to document anything about this TM. I had to start from scratch with coachings and corrective actions and it has been a long and painful process that has damaged my DTK scores and team morale.
Bottom line- If it is not put into writing, it does not count. I tell my TM's if I am documenting a conversation and if another TL starts to tell me about a conversation they had with one of my TM's I ask them to put it on paper if they want anything done about it. In nearly three years as a TL, I have only had one fellow TL follow up with a written document.
A good TL will let you know when you are being officially coached and when you are just getting some pointers on how to do your job better.