My initial instinct would be that it's simply, that everyone has the Zombie bug already, and no matter how you die, you'll become a Zombie, wether bitten, gun shot, natural causes etc, since that is common in Zombie lore these days.
problem is, by Rick not sharing this, he could put others at risk, for example Lori cuddling Carl as he's dying from the gunshot wound, if he had died in her arms, he could've turned and bit her. Would he withold that information? Is it OK for him to withold that information, since people don't turn immediately upon death in this show's Universe? Or does this rule out this possibility?