The DOT states that this rule applies to "each U.S. and foreign air carrier that has a website marketed to U.S. consumers," so as you've found, it doesn't apply to OTAs or other travel agencies.

Even so, some travel agencies voluntarily offer a similar refund rule as a matter of policy (and then only for some airlines but not others), so if you purchase through a travel agency (OTA or otherwise), you have to find out their specific policy on refunds for the itinerary you wish to purchase.

The last time I purchased a ticket from an OTA and was due a refund, it resulted in a similar round of finger-pointing between the OTA and the airline. I always try to buy tickets directly whenever possible. Glad you were able to (finally) get Priceline to refund your ticket!