Unfortunately, this sort of thing happens all the time. There are 2 issues here causing this problem.
(1) The rate shown on the receipt, mistakenly given to you by the hotel, is not a rate generally available to the public. They gave you Pricelines receipt.
The hotel has accidentally given you Pricelines receipt, showing the rate that Priceline paid, per room, for hundreds, possibly thousands of rooms for that month. The rate you were charged for your room, by Priceline, is the rate you agreed to pay, based on the offer price YOU NAMED. Since the rate shown on Pricelines receipt, mistakenly given to you, is not a publicly available rate, and is not posted on the internet as such, it would not be considered valid for a "Best Price Guarantee" claim.
(2) Customer didn't read or doesn't understand the "Best Price Guarantee" provided by Priceline.
In laymans terms, the guarantee states that Priceline guarantees the customer wont find the same hotel room / night ... posted at a lower rate anywhere on the internet, within 24 hours of your purchase ... and if you do find a lower rate POSTED ON THE INTERNET, within 24 hours of your purchase, they will refund you the difference (and they're not going to just take your word for it, they're going to have to go to the internet to see if a lower rate really was posted somewhere).
Since hotels generally dont allow you to check the rates for nights already passed, they would not be able to verify a lower rate on the internet after your check in/out dates have passed.