I agree Bill... that and all about Tyreese's overall personality. He wasn't much for the action. He was capable, but didn't want involved and ultimately distanced himself from that, so I think he lacked some of the experience.
He was focused on Noah, in Noah's home, just seeing Noah's mother and brother, thinking about Sasha perhaps... plus I think he maybe (and again, lack of experience perhaps) was thinking the one behind the door must be trapped, and didn't think he was in as much danger as he figured. Perhaps it was a whole other walker too, and he figured they'd accounted for the 3 family in the house (dead 2, and other brother behind the door), so he let his guard down even more?
Walkers do seem awful sneaky though... For not having coordination and stuff, they sure do just sneak up on folks, routinely. Outside even, in piles of brush.
It seems like a rarity where a Walker gets someone though, in such a simple manner, but I think it's sort of an inevitability too. To remind everyone the Walkers are as big a threat as they ever were, and people may be worse, but threats are all around.