I bought my grandmother's house in CA and yes, I was able to keep her tax basis. However, it may be that it technically passed to my dad and then I bought it from my dad. I can't recall, exactly.
We paid FMV minus the fees we likely would have paid a lawyer. We did hire someone to help with the transaction. The person was an re agent and also a loan broker, I think. (We didn't have a loan. It was actually financed from my parents, but we did an official lien and everything else.) We wanted to make sure the paperwork was solid, so we paid them a flat fee to do everything they would do for a regular sale. (It's been a long time, so I'm fuzzy on the details. But I think we paid $1000 and that covered everything--the lien, then transfer of ownership, the title insurance paperwork, etc.
Also, the prop 13 "inherited" basis is different from the tax implications of selling for less than FMV and that being seen as a gift by Uncle Sam. Ours was close enough to FMV and we could justify the price if asked, so we didn't worry about it. But if we had paid significantly less then FMV, we'd have treated it like a large gift and filed the necessary paperwork (so dad would have paid a gift tax, but actually not because he'd have just filed the paperwork to kick that can down the road, basically.)