"Maybe" and "probably not". I don't worry overmuch about the firearms "crisis du jour". The internet "experts" are all over the place on this subject. Most of the accounts appear to be based on a few genuine instances of weapons firing out of battery, a lot of hyperbole, and the usual "repeated ad nauseum until it has become generally accepted fact". Objective analysis has shown most of these incidents to be caused by faulty weapons (filthy dirty, bad headspace, or broken components i.e. firing pins w/protrusion) or lousy QC of reloaded ammunition (usually protruding primers and out-of-spec headspace).
Most military rifles have an inertial firing pin that floats freely within the bolt. The force of the bolt closing will sometimes impart sufficient momentum to the firing pin to dimple a primer. ANY PRIMER! Check for yourself the next time you clear your rifle. If the weapon is clean and the firing pin moves freely, it's inevitable. Primer manufacturers know this and make allowances. Grab 10 rounds from different manufacturers, chamber them all, and each one will have slightly different imprints. It's not a big deal, primers aren't so sensitive that a sneeze will detonate them.
If you're concerned, you have two choices: shoot only military ammunition; or order milspec primers for your reloads. (CCI makes extra money selling their contract overruns packaged for civilian sales - check Midway) Otherwise just watch the QC for your reloads (NO PROTRUDING PRIMERS! and proper headspace/trim to length) and keep your weapons properly maintained. I would recommend discarding brass after NMT 4-5 reloads, semi's abuse it a lot more than bolt actions. Head separations are annoying, NTM dangerous.
I need to check the suppliers a little more often, your Hi-Tech Ammo link was already out of stock.
HTH - Peregrino