I've now encountered this, and it's definitely a bug. I had to take a bunch of newly-minted squaddies on a Council mission while my main team was wounded; I lost an assault and the sniper was critically wounded. The mission completed screen told me I'd lost one soldier, however both the assault and sniper were shown as KIA on the following summary screen.
At least now I have justification for redoing the mission since it was bugged...
I've also lost soldiers to an annoying critically wounded bug when the game's telling me a soldier is bleeding out and has X turns left, but they don't have an onscreen health counter and aren't recognised by soldiers with medikits - I lost a good support squaddie that way, since even with the remaining medikit squaddie standing on top of her I couldn't persuade the medikit there was anyone there to stabilise.
Are you sure that you were on the same level of elevation as the wounded soldier? From memory, even if you are like one step down from the wounded soldier and right next to them you still cannot heal them. The same goes for stunning i believe.
I tended to play aggressively pre-Meld as well, mostly because it makes for a better game but partly because the all-overwatch tactic was never especially reliable at keeping people alive anyway. Now that Seekers exist - apparently introduced precisely to defeat this tactic by drawing all your overwatch fire before dangerous aliens arrive - it's less reliable than ever, and aliens do seem to cluster a lot more.
I actually find seekers a bit of a joke, and over watch is actually (IMO) the best tactic to kill them (excepting throwing a battle scanner, which is the best way). When you trip them, bunch your whole squad up behind cover close together and stick them on overwatch. When the seeker de cloaks, it will get a barrage of shots and be killed. Keep overwatching until they are all dead. Simples!
I am of the opinion that the base assault should always be done immediately after you get armour and lasers. The reason why i say this is that the only hard counter to elite mutons is a mind controller. 3 elite mutons can be a real pain in the arse if you dont have an experienced team. In order to effectively counter them you need a psi soldier, and for that you need base assault. By the time you have built the psi labs and found a soldier and levelled them up, you will probably be at the point of elite mutons. They can do a ton of damage too, much more than regular mutons. Its possible for them to outright kill a soldier wearing ghost armour in one shot.the base assault
Because the base assault scales with where you are in the game, there is not really much benefit in waiting. The only thing that changes is that you have to deal with sectoid commanders in UFO's instead of overseers (and get through the mission of course). For that laser weaponry is sufficient.