They 'spin' the priming compound into the rim of the case. Sometimes a spot or two (or more) doesn't get any priming compound, so when the rim is struck, there is no ignition. Yeah, I go ahead and rechamber the round and fire it off. If I get more than two or three solid firing pin strikes and no ignition, I usually just pitch the round (dud box, if available). I'm not stubborn enough to keep trying to light it off after that. As long as you aren't seeing light strikes (unusually shallow impression from the firing pin), it doesn't matter what the gun is -- it's strictly the priming. If you have a complete strike and no ignition, it wouldn't matter if you'd hit that exact spot with a punch and a 10-pound sledge -- it wouldn't have fired.
If you are getting light strikes, check to see that there isn't anything keeping the round from fully chambering and the action from fully locking (residue, etc.). If that's okay and it persists, check the firing pin channel for residue/obstructions/burrs.
Haven't shot a lot of Federal or Remington, so I'm not sure about the rate of misfires noted in some of the posts. However, I have shot a lot of CCI (mostly MiniMag solids for target and HP for small game) and I've had very few that don't light the first time, which seems to match up with several other people's experiences.