Bulbasaur, it's not a case of 'paying for half of something' any more than renting a house is buying it. It legally belongs to the person paying off the mortgage (unless they default and the bank repossesses); anyone else is a tenant. And why not? The OP would still have to pay for rent and utilities wherever she lived, it wouldn't entitle her to a claim on the property she'd been renting!
No, she wouldn't own it if she was renting, but she would also have legal rights to her tenancy if she was renting.
If I rent a place, I have certain rights regardless of whether the landlord loves me or hates me. I can't be thrown out on a whim, I have to be given notice, and I have a contract that states how long I will be staying.
With a house, that's not the case. She is at the mercy of her DP. If he packed her bags and kicked her out with no warning, she has no legal recourse and he'd be legally allowed to do so.
So.. again. No, I would not pay for rent in a house where I was not getting renters benefits. If my DP wanted me to pay rent, I'd want a contract of sorts so I wasn't there merely on his good graces. Even people that rent out rooms in a random house have more security than she does right now.
Utilities I could understand since she does use half of those. But a house she has no legal rights to, or legal staying power, no way.
Personally, I had my own place until DH and I got a place where we put both our names on the paper. I wouldn't do it any other way.