That should be enough proof. If she denies giving you the horse you always have that against her. Though, if you can I would ask her to sign the horse over legally. Tell her you're getting the vet out..
I am missing what the big deal about signing a contract is?
You should want a contract. It will clarify all these issues so you will not have any trouble in the future.
The horse world is a very small place. Packing the horse up and moving it before the 'rescue lady' comes by might work for now (though it is kind of low on your part) but in the long run it only makes you look like you are doing something wrong and you will be found.