Would it require extra programmer effort and cost to develop such export functionality? If they didn't invest the money to build that capability, why would they want to? What's the ROI for them to do it?
It took several years for GMail to have mailbox export capabilities. Some team somewhere has to write and test all that code.
They are (correct me if I'm not understanding how this service works) the only ones in a position to know which short URLs are already used and which ones are not.
So, if the list of short codes is short enough that he can search it in a couple of days and follow all of the links, then that's obviously what he should be doing rather than having public gripe time on HN.
(Then again, if he pays them just once he gets a decent bit of extra time, and they get paid for providing the service when his business was too small to justify him bringing his own infrastructure. Win-win?)
Sure it sounds unfair when you say "they won't let ME export MY data", but it sounds different when you say "we'll provide a FREE service for you, up to a point, but when it gets reasonably large or commercial you promise to give us your business."
There is no such thing as a free lunch.
Removing any "shady" or "not cool" accusations (and implicitly leaving them to the reader), and just adopting a neutral "Hey devs, make sure you read the ToS, 'cause I didn't and look what happened..." tone would make your piece basically unassailable.