Piggy is complicated. She is a diva, she can be self centered, and she can come off as being uncaring, but she really does love her frog and deep down (really deep at times) she cares for the other Muppets as well. Yes, she'll karate chop anyone who rubs her the wrong way and she often comes off as being somewhat mean, Piggy can also be sensitive and concerned about others. She just has a very reserved way of showing it beneath her diva exterior.
To say that it is out of character or bad writing for Piggy to have her leave her friends in the basement wouldn't necessarily be true. But I think that if Kermit spoke up about it being an issue, she might have (reluctantly?) stayed behind. Though if it were a more serious situation, I think she would have stuck with them.