Squating what does squatting have to do with this.
Squating refers to a person or group of people who settle on someone's land without any legal authority and try to claim land as thier own.
Re-read the facts and don't skip the parts about:
1. "... Last night, I met with [the] tenant and the landlord, chatted for awhile, and signed the lease and paid the pro-rated rent for the rest of the month. ... I thought the deal was sealed."
2. "... Today, the landlord decided not to rent to me and she came by and returned the check for the rent [to me] ..."
If anything, the landlord unilaterally reversed (either cancled or breached) the agreement for the lease.
The landlord can not have it both ways. They can't unilaterlly cancle your leasing agreement and then collect rent from you for the cancled leasing agreement justs because it has your name on it. That is absurd.