I will weigh in a little here. A few years ago I installed a nos replacement Sealed Power rocker arm set on one of my 261 motors, and a set of NOS TRW replacement push rods. What I did not do, mostly because I have never had any issues, was blue up the cups and balls with Dykem and work them in by hand to make sure the ball was fully seated in the pushrod cup. In this case, they were not with the adjuster ball being ever so slightly larger than the cup and so the ball was partially seated with the majority seated on the rim of the pushrod cup. And yes, you guessed it, broke the cup on the pushrod after about 100 miles.
So I bit the bullet because I just don't want that kind of hassle these days so I ordered a set of Smith Brothers pushrods and adjusters. More expensive yes but here is the thing. They will not bend, they are straight as an arrow and the ball adjusters and cups are machined to very tight tolerances for full seating. They are really great quality. I can be pretty hard on my motors and this particular 261 is no exception. I can report not a single hiccup in 10 years.
Here is the other thing, their adjusters use a hardened hex adjuster and hardened multipoint adjusting nut which means you can use a standard small block Chevy rocker adjuster tool that will not slip off like a screw driver. Makes adjusting the valves a little more comfortable.
Otherwise, I am with 52Carl, if the adjuster nut is running smoothly, use it.