Sometimes in order to provide the perceived necessary correction, the design of the filter suffers from stored energy problems that were either not understood or simply ignored. With a tube amp, this would not be a problem but clearly it can be with other amp topologies.
It's not just minimum impedance, it's the storage of reactive energy. Filter responses contain both capacitive and inductive slopes (leading and lagging current responses), these factors plus stored energy can allow destructive oscillations to occur depending on amp topology and even specific design approaches. They can be especially troublesome on class ab amps using high global feedback and low stability margins, as well as class d topologies.
I don't have a formal background in electronics, so am at risk of being "that guy". I try to keep my impedance curves fairly benign (above as well as within the passband) in both magnitude and phase angle, and use damping resistors on the parallel legs of my filters so they don't show a dead short if a driver blows, but I don't know what specific steps to take to avoid the stored energy oscillations you describe. What should I be looking at? What are the symptoms that might show up in measurements (before the magic smoke escapes)?
If this is beyond the scope of what you're comfortable discussing here, no problem. But I really don't want to be the speaker guy who accidentally kills someone's amp.
Will's ears perk up as he anticipates one of those crucial bits info that keep his triggerfinger perched over the "remember this" button.