The general rule throughout the United States is an employer can set payout policy for PTO upon a voluntary quit. Any exception would need to be in state law. If I recall right, a law was proposed in 2010 which might have impacted PTO in Utah, but I don't believe it passed.
The best source for learning what Utah statute and regulatory law says when you don't have an attorney to research it for you is probably the Utah Labor Commission. Their current web page for Q&A regarding benefits says:
"In general, Utah labor law does not require an employer to provide benefits to its employees. If an employer does establish a policy or practice of providing benefits they are expected to abide by the policy or practice in a non-discriminatory manner." http://laborcommission.utah.gov/FAQ/wages.html#vacation
You indicate that other people quitting this employer have been paid PTO. That seems the most likely argument for you to also be paid your accrued PTO. By refusing to pay you, your employer is obviously abiding by its written policy. The problem is, your employer will never be able to apply its policy in a non-discriminatory manner because the policy itself says it will be applied in a completely discriminatory manner. First of all the policy is that PTO "may" be denied. Second, it's left up to the company's "sole discretion." Those words are reckless in terms of setting policy and basically are begging any Labor Law attorney who reads them to come and sue.
I recommend you contact the Labor Commission and discuss this employer's policy with them.
PO Box 146600
Salt Lake City, UT
You might even consider filing a claim with the Labor Commission.
PO Box 146630
Salt Lake City, UT
You could also consult with an attorney who specializes in labor law. However, given the small amount of money we're talking about in your accrued or banked PTO, don't be too surprised if you can't find a labor law attorney who would be willing to go after it for you. Nevertheless, you won't know till you ask. And a consultation might be worth the effort, if for example, the Labor Law attorney believes it's an issue worth pursuing, and, there perhaps is a law which allows for attorneys fees in such cases. (I don't know that there is, but again, it can't hurt to ask.)
Small claims is also an option. But be sure to track down the statute and/or regulation which requires an employer to apply their policy in a non-discriminatory manner. It's unlikely the small claims judge will be familiar with it. Ask the Labor Commission for the citation (which you can then look up on the internet) and anything helpful which they might have on a web page or in writing.
I hope this information helps