I was also surprise to see "Premier Access" on my boarding pass yesterday too. I do not fly to the US all the time.. so I am not sure if it is normal we get that on the boarding pass.
Premier access just means they're recognizing your *S/*G status. That's totally normal. Yeah I used to get Group 3 (or maybe 4?) -- but the last couple of flights I also got Group 2. It's been going on for at least a month.