You are right. Same with any third party hosting provider. You have to balance the cost of hosting the pictures to your own server with the risks.
On the other hand if you can't afford hosting the pictures on your own infrastructure, you have to balance the fact you have a single point of failure in imgur with the fact that without an official upload function your user would be encouraged to upload them somewhere else with the risks of broken links if said users remove the pictures later on.
FWIW there are tools to download imgur album. You could run these tools on an inexpensive NAS server at home which would give you a cheap backup and an option to host them somewhere else and convert broken links if imgur goes bankrupt in the future.