Can A Property Manager Cancel My Lease For Negative Online Reviews?

Location: Denton, Texas

I am moving into a new apartment this week. However, I had some issues pushing my lease start date. I called the leasing office to ask if the lease date could possibly be moved, and the office staff confirmed the possibility, noting they needed to get it confirmed by upper management. ​A couple of days went by and the leasing document was sent to me. I signed the documentation, indicating my commitment to the lease; however, the lease date had not been changed on the contract. I emailed the staff again and received no response. I called again, and a staff member confirmed the possibility of it being moved again depending on what upper management said. The staff member indicated that the upper management in question was out for the holidays and that they would notify them as soon as they were back, with no indication of an exact time. ​I sent an email on December 31st asking if the lease start date could still be pushed and received no response. I called the office again, and upper management told me that they are not able to push the lease date and declared that my application will be canceled if the rent is not paid by the original date. I made a complaint about the situation on Google reviews and other websites. After a request by leasing staff to take down the review, upper management called me and said that they are canceling my application due to me being an "unhappy customer.” What policy enforces this motion if it's valid?