The pulse thing is just more of an indication, or factor that may help point to a TOS dx.
There's a small percentage of "normal" or non TOS folks that will still lose their pulse at certain arm positions. So pulse loss or not on it's own doesn't prove much, it's a cumulative process of adding up all tests & all symptoms. And also one of ruling out other possible causes.
Some drs will do quick 1 time single positional pulse test and only go by that result..

that is not a comprehensive exam...IMO.
scroll down to center of this page for more info -
http://www.nismat.org/ptcor/thoracic_outlet
I had 1 MD that did a very brief single pulse check on my rt arm - my sx were worse on the left, so I think she should have at least tested both sides and done more than the 1 test.

( I was just starting to find out about TOS at the time, so didn't question anything)
later on -after I had learned more about it -
Chiro & the 2 advanced PTs did do all these and also the positional tests to verify if the c spine might be a cause of arm pain & sx.
Although I did mention/ask if it might be TOS or something like it - to make sure they did do them.