Yes, fresh is best, but it's far better frozen than with preservatives. I think that Five Guys and a handful of other places just say that as part of their BS marketing...when you squish a burger that flat and cook it that much, there's no real flavor left anyway. It doesn't really matter what quality of meat they start with...it all tastes the same when you cook it like that unless it's really, really terrible.
I have some local farms I buy from, as well as more normal places. Grass fed/finished is better.
I don't actually eat burgers anymore, but that's because I don't really eat carbs and don't like any of the bread substitutes. So, normal for me is super-thick, rare reverse sear over grass-fed butter, bacon butter, or tallow, often with some combination of grated aged cheese on top and diced jalapeno mixed in, sometimes a slice of tomato. Always with quite a bit more salt than you'd expect the day before (if you give the salt time to soak in, you're salting the whole thing, not just the surface).
Seriously, it takes about 24 hours to properly prepare and cook a burger. But most of it is waiting around for the salt to soak in and getting rid of the surface moisture.