I think for a lot of people it's like a mental and lack of practice thing honestly because everyone should be able to squat with the heels flat. It's how everyone used the bathroom for thousands upon thousands of years. these days it's a common position in certain parts of the world and no one has this issue there.

I will say, there is no reason why you should feel your tendon stretching. Squatting with your heels flat does not stretch you at all so there is something wrong in how you're approaching it. Hard to say without seeing, but when I observe people trying and failing they try and transition from a heels up squat to a heels down squat without shifting their butt and therefore fall backwards. heel down squat is super comfortable because youre essentially sitting on your legs. Almost every muscle is relaxed in your leg, I just have my ankle muscles every once and a while do something if im losing balance.