Yes, she does bear a striking resemblance to their lead singer. I had never paid attention before. I like the Scissor Sisters as well!
As for the rhyming, that’s pretty cool. I had to look to be sure, her name is not a stage name, Balk is her mother’s last name, so it is just happenstance.
It did remind me of another Veruca Salt that I enjoy as well. This is one of my favorite songs of theirs, these lyrics always striking me as interesting.
Keep her down, what a lovely daughter.
Oh she is not born like other girls,
but I know how to conceive her.
Oh she may not look like other girls,
but she’s a snarl tooth seether