It's sort of a double edged sword. On one end, I agree. The other side is that if you do live together, she is paying a part of your mortgage and is supporting the home. I believe that she should be entitled to some amount of equity that is gained while living there. I'm not saying half or even a huge amount, but a portion.
For example, say you buy a $hithole and plan to fix it up. The lady moves in. While you're doing the work, she is likely cleaning, cooking, possibly even helping with the work. She is providing the man with more time and resources to get the improvements done. I don't think it's unreasonable for her to get a portion of the equity if the house were sold. Most here likely won't agree, but to me, it seems reasonable and fair...