"He likes her dogs."
Translation:Han tycker om hennes hundar.
sina is gender neutral, yes, but it always refers back to the entity which initialised it. So in han tycker om sina hundar it always is the same person who likes the dogs and who owns the dogs. It cannot refer to a separate person. If it were hon tycker om sina hundar, it would be a female who liked her own dogs - never somebody else's.
The sentence he likes her dogs would be han tycker om hennes hundar - with no exceptions for sina.