Yes, they do. The "Max HP" on the character sheet is not your real HP allotment, nor even the maximum with temporary HP sources. You have access to a lot more HP, depending on the number of surges you have, you just need to tap them. A character with 32 "regular" HP and seven surges has access to roughly 103 actual HP in a day. (32 base + 7*8 surge + 15 (1 short of negative bloodied). This can go up based on healing from negative, temporary HP and riders from leader healing.
These are the actual HP a character has to use. Your view is oversimplified and simply inaccurate. The background feat, toughnes and durability can all help mitigate a lower constitution, but it's at a steep cost. It's not bad, overpowered or "broken", it's a build choice.
One last time:
Read what I actually wrote. Arguing a point I'm not even making is foolish.
I never contended that dumping CON and taking the background was good. The
ONLY (and I don't know how many more time I have to say it) contention I was making was that if you're
already dumping CON, then this background can effectively replace Toughness. Therefore, for certain characters, it's effective is equal (if not superior) to a feat. This is too strong when compared to the other backgrounds which, as I already explained, give benefits
less than the feats that most closely mirror their benefits (ie- +2 to skill compared to skill focus, add skill to class list compared to skill training, add a single language compared to the language feat that grants 3 languages).
So, if you're going to continue to be dismiss and tell me that my view is "oversimplified and simply inaccurate", then why don't you try actually discussing the point we're talking about. Obviously raising CON will beat out Toughness, Durability, this background, and just about anything else that raises HP
every time. However, not every class can afford it. A Wizard multiclassing Warlock, for example, wouldn't be able to pump CON because they're already pumping two attack stats. Neither would a TWF Ranger that's concentrating on STR and DEX for attack and AC separately. I could go on listing all the potential class builds that dump CON, but I trust you understand the point now. FOR THOSE CLASSES this background is strictly superior to Toughness because it grants almost the same bonuses while at the same time saving them a feat slot.