PhD program turned into Bait-and-switch
If you can't afford it, you can't afford it. Do not lie to another school, just tell them the truth, without the words "sham" and "bait-and-switch" etc. 

Tell them you attended for one month and withdrew, and can prove that, but there is now a dispute over tuition, which you thought was waived. They want you to pay 20K, which you are contesting, so they will not send you a transcript for the one course you signed up for and dropped after a month. Also tell them there will be no grade for that course, you formally withdrew, and that is all the transcript would say.

Lying to a new school will get you into trouble THERE too. Be honest, with just the facts, so they can't say you kept this a secret from them.