add_action() and add_filter() are the same function. If you look at the source you’ll see that add_action() just calls add_filter(). So yes, this it is technically possible to register a filter callback with add_action().
The difference between an action and a filter is that filters expect a return value, while actions do not. This is important when defining the hook with do_action() and apply_filters() because do_action() does not return a value. When it comes to registering a callback the only difference between add_filter() and add_action() is the name, but it’s a good idea to use the right function so that it’s clear what your code is doing. But if you make a mistake and use the wrong one, as this plugin has, it’s not the end of the world.