I agree manual trimming does not help increase your turn rate. However, when it comes down to it, combat trim is constantly adjusting your trim to attempt to go straight when there is no stick input.
In general as you slow it will trim more elevator. In a turn with quick stick input this can work aginst you. If you are already pulling your elevators to the edge of a snap stall, and combat trim is trying to adjust to your speed decrease, it can push you over the edge.
In a sustained turn within your envelope it doesnt make a noticable difference, but I think you will find that a quick brake turn in one of the non-TnB planes is more effective with manual trim as well as when riding the edge.
I think this effect is what leads to the myth. The issue isnt turn rate, but possible instability caused by a limited auto trim.