Not true according to some studies. Exercise has been shown to have physiological benefits beyond addressing issues about how things look.
I'm no less self conscious about my body in terms of looks now I'm not fat compared to when I was nearly (perhaps actually) obese - I didn't care then and I don't care now, and where I have problems with people I've never thought it was my looks that put them off.
While I don't suffer from social anxiety specifically (I have it, but in "normal" amounts except where cause by the issue I'm about to mention) but I find the symptoms of bi-polar disorder less apparent (or more apparent less often) since improving my physical health and sometimes when they do rear their ugly heads "going for a run" or similar can help.
> Exercising won't solve ... anxiety due to stammering or have scar on your face.
I don't think the last poster was referring to anxiety resulting from such causes (though they were not clear on the matter).
> Exercising won't solve stage fright
If you specifically mean stage fright due to normally stressful situations (work presentations, actually being on a stage, ...) then no, though generally feeling better about yourself can help more generalised social anxiety.
He's not alone. Most medics do too.
The only way I managed to get off alcohol was by vigorous exercise: cycling many miles and hours in the Yorkshire Dales. That was in '98.
Before that, I found that any stress or anxiety would quickly result in me going back on the bottle.
My uncle was a general practitioner for many decades and he reflected later that at least 50% of his patients presenting with primarily a physical complaint, he'd find the actual pathology, if you did enough digging, was actually primarily psychological in nature.
This is conjecture.
I have anxiety surrounding public speaking. Exercise helped with baseline anxiety, now I rarely feel like anxiety is a roadblock when I anticipate speaking.