Are these really considered compliments for a woman if said by a man?

Neither of them seem like compliments. First one is comparing you to a dog, and stating that regardless of how bad a guy treats you, you'll stick with him. Only a person with low self esteem would do such a thing. If a guy cheats or abuses you, you should leave, not stick around like a dog. As for the independent one, that too isn't really a good thing, considering guys don't seem to like independent women, and tend to be turned off by independent woman who give them a run for their money.