It's definitely a website problem right now. My mother, who is a total non-elite, traveling to DEN on a X fare was able to grab an exit row seat on the website last week for a flight in September. She was not even logged in under her OnePass account.
For anyone other than Platinum elites, until the new website was launched earlier this month, exit row seats were not available online. Since the new website was launched, exit row seats are available online to a lot of passengers who are not Platinums. In the past, Golds and Silvers could get advance exit row seats, but they had to call for them, or do it at an airport ticket counter. They could not grab exit row seats online.