I wanted to try on a pair of LaSportiva Miuras and the store didn't have my size in mens. They gave me the womens shoe to try on. I was told that they often recommend the women's shoe to men because it doesn't stretch as much and it is much more comfortable. Is there any truth to this or were they just trying to make a sale?

no.
thats bull dookie.
Womans shoes are lasted different. They have less volume and a narrower heal. the arch is not as drastic either. I wear womans muiras becuase i have low volume narrow feet. They will stretch the same as they are still using the same materials and contsrtuction. just different lasts.
Length wise they will be pretty comparable ( womans vs mens_) but if you find that your foot is screaming to burst out of them in other places the Mens is the best chioce for you.
hope that helps.

With this in mind^^^ if one has a low-volume foot + narrow heel, don't hesitate to try on women's models if they're offered in a style you'd like to climb in.

Yeah. agree on that.

I climb in womans miuras and katanas due to that very reason.