You'd think that but because you're working with both axis it tends to work.
There are plenty of videos documenting people ripping a filter to pieces and having only the mounting plate to work with. Here is one example:
The rope trick solution was much, much less problematic and it worked just fine. No surgery required. Now I have a tool that, just in case this happens again (unlikely - I do my own work, lube the filter gasket, and don't torque the filter on with a anything other than my hands), I won't be nearly as bothered or challenged.