chrome 20" factory wheel

I have a 2012 1500-Ram Sport, Crew Cab with 20" factory mags. I want to put Nitto Trail Grappler M/T on my factory 20" mags and NO wheel spacers; I also want to put a 2.5" level kit DayStar in the front only. My question is that my local tire dealer says that 275/65R20 is not going to rub but...