Just because it is labelled AAA doesn't mean that it will be a good tender steak.
My understanding is that the labelling has more to do with fat content than quality.
It could be an old milk cow that reached the end of its career.
Mechanically tenderized means the meat has been pierced by 100's of 'needles', and it does make a more tender piece of beef.
Unfortunately, the same process can drive any e-coli or other contaminants that are on the surface of the meat into the middle of the meat.
Hence, if you like a rare or a blue steak, you may be ingesting the e-coli, that normally resides only on the outside of the meat and is killed off by the heat when cooked.
That is why they put the warning on to cook it to a minimum internal temperature of 63C/ 145F.
Warning was probably written by their lawyers.
Best to avoid the mechanically tenderized meat and cook real meat the way you like it.