Just because cops are saying it doesn't mean it's not true. There's actual studies on the matter and they've done testing. Drawing a firearm and shooting accurately enough times to consistently disable a human immediately - so at least two shots with handgun calibers - is extremely difficult and cannot be done consistently within that range or closer, and again most self defense starts within or just outside arms reach.
That's a large part of why they themselves teach police basic grappling. Most of them aren't any good at it, but they are still taught it for good reason.
Again, it's a matter of consistency - if you try to draw a firearm when someone has hands on you, they are GOING to attempt to stop or disarm you by grappling you, even if likely in a clumsy untrained way.
Obviously, it's much easier to resist grappling when you yourself know how to grapple. It's a skill, after all.
Not strictly martial arts related, but I think I've done a lot of good work on the mental shit that's been impeding me from actually properly getting into DOING it consistently instead of just reading about it, as I've been wanting to do since I tried the local HEMA club just before thanksgiving.
If I can get the financial shit in order, I ought be able to go consistently, and being on disability I could take full advantage of the crazy amount of classes they have for a HEMA club. Not exactly practical but it's the thing I would be most inclined to do most often, for reasons both of my personal interests and the fact that HEMA has probably the most trans-friendly culture of any martial art, at least in the US. And hey, they teach the grappling stuff from the manuscripts and also host a Latosa Escrima class, which seems quite practically-minded even if most of the practice is still done with weapons.
Fingers crossed that by next month I will be able to start doing this shit in a proper committed fashion.