Ok, I've wandered through the code and think I've found the issue.. the weekly stats from WU have precip-total at that hour, and the routine that was totalizing the rain amount was expecting to just sum-up all the values (which works for the day, month, year).
I added a function to get just the end-of-day totals for each of the last 7 days and sum that up instead.
Try the attached version 3.4g of WU-History-inc.php and see if that fixes your issue. It also removes the Custom link (since that is not going to work either).