Michael, if that's rimfire ammo, there might be a very slight danger of detonating the primer as you tap down on the bullet, so forcing the rim down on to the bench. If that happened, the rod and bullet would make a hole in the ceiling.
Centre-fire shouldn't have that problem, of course.
Cheap ammo can, as you say, be a bit variable on diameter. I use good quality RWS or Lapua in my .22 target rifles. I went off Tenex when there was a rumour that Eley were putting ground glass in the propellant to control the rate of burn.