I must not be above their content storage limit or my account is old enough that they haven't squashed "hot linking" yet.

http://photobucket.com/terms

Quote:
Last revised June 28, 2017

Free account : Each individual Member gets one free account that provides 2 GB of free storage or space available for your original photo files, or videos under 10min. The free account does not allow any image linking or 3rd party image hosting. If a free account Member exceeds their Content Limit, their account will be immediately suspended and they will need to become a “Paying Member” (defined below) in order to continue accessing their account. You can upgrade to a Plus account at any time.