What defines a rare exception? The Doctor's regenerations have been all over the place. Otherwise we just have Jenny, Romana, The Master, River, and that one guy who was hanging with his next incarnation. Also, with the fob thing, how do we know what happens when they die in that state?
If the rule is a new body, how do you account for those who seem to be able to determine their new form? Romana chose to look exactly like Astra. The Time Lords offered the 2nd Doctor various choices. Who's to say that couldn't be the same one?
What you're doing is starting with a desired conclusion and constructing arguments to justify it. That's backward reasoning, because you can use it to support any position, no matter how wrong or nonsensical. Better to reserve judgment until we have more evidence, then formulate a hypothesis based on the evidence.