OEM Rocker Arm Side Play

There is a fundamental difference between a roller rocker & a stamped factory rocker.
The roller tip on the roller rocker is not very wide & there is little leeway for side-to-side clearance before the roller runs off the valve tip.
The contact area of the stamped rocker [ in comparison ] is quite wide & has a lot latitude as far as side clearance goes before excessive side clearance [ on the shaft ] causes a problem.