This kind of statement bothers me for several reasons.
First, I have killed PCs in at least 5 editions of D&D, 6 if you count 3 and 3.5 separately, and it is not significantly more difficult to do so in 5e if that is your goal.
Second, DMs who make statements like this usually don't really use the rest and/or death saves mechanics properly. Remember, you only regain up to half your HD on a long rest, making several days of tough battles linked together significantly more difficult. Similarly, striking a creature that is already down is 2 automatic failed death saves. In a world where PCs are known to bounce back easily, why wouldn't you make an effort to land a couple de gras? It's what you would have done in the "good old days."
It is pretty easy to kill PCs as long as you keep attacking them while they are down. As a DM I always do that for intelligent enemies. Once a PC goes down the enemies try to get to him or her and kill him before another PC can bring him back. I have even had an enemy take an AOO so he could go kill a PC who was down.
A lot of DMs don't do that and concentrate on players that are still up. That is a tactical mistake though because downed PCs are almost always brought back into the fight before the next turn even comes around, often without the party even losing an action, and intelligent enemies should realize this is going to happen.
It is kind of like when you are watching a horror movie and the BBEG goes down and the protagonists hug and cry or run away instead of taking the shovel they just downed him with and bashing his head into a bloody pulp with it while he is on the ground. My monsters are not dumb like that.