Is any amount of wobble unacceptable?

Hey r/bikwrench, I recently “refreshed” this wheel set by replacing the bearings and free hub body and hub internals. As an additional step just to be thorough, I brought it to a local bike shop to have it trued as I don’t have the tools and skills for it.
The bike mechanic said we had to replace the nipples as the stock ones on the dt swiss wheel sets are made of aluminum and is already disintegrating when he tried to tighten/loosen them. They were replaced with brass pillar ones. Now here is where lies my dilemma, the bike mechanic says that the tire (less than 200km) is unbalanced and causing the wobble. Can the tire be really the culprit? Is the wobble acceptable? Or should I find a more experienced wheel builder or there are instances that a wheel can’t be trued 100% straight?