Yes, strictly speaking that is correct, a letter is not planning permission.
However....
When you come to sell your house, the situation I gave, the purchaser's solicitor has his boxes to tick and his insurance to protect. A letter will almost certainly satisfy him. If it doesn't, then you go get your lawful development certificate (LDC). So having a letter means you lose nothing and could gain a lot and it's a overall less hassle and usually cheaper.
Another scenario would be if you got your letter, built your extension to the plans submitted, then the council decided you needed planning permission all along. If that was me, and the possibility is remote that planning would actually try to enforce anything, I'd fight them all the way to court where I would win.
Or you could say 'sod the lot of you' and build it under permitted development and tell nobody. This is perfectly legal and the permitted development definitions are quite straightforward and the OP appears to understand them. You cross the selling bridge when you come to it. If four years have passed then you will get your LDC anyway, but it could delay a sale. In this buyer's market I think it's sensible to have something in writing in advance, others might not feel that way.
So getting a letter is sensible if the council provides them. It's what I do, got one a few weeks back, and although it does have caveats as long as I build to the plan the council has no chance of any comeback that will stick. And in any event, what I am doing is 100% permitted development, so they would be told where to jump even if they did.
As always, you need to decide what to do, it's your house, but it's good to know of your options.