You're not exaggerating the risk as far as what would happen to the object that managed to get jammed in to a fixie drivetrain at speed. You are perhaps exaggerating the risk of that happening, though.
I don't see many objects managing that feat, without serious planning on someones' part, and unless it's flesh and bone, or something that was hard enough that the chainring wouldn't cut through it, then there would be minimal harm.
If a stick gets caught in the chain ring, it will get cut in half. So what if it does? Nothing will happen to the rider, and even the chance of damage to the bike is minimal. Same thing with brush. Unless it's large enough to stop you pedaling, then it's not a problem. And since fixies are rarely ridden off road, the chance of these 2 things happening would be pretty remote.
I've had my pant's leg get caught in a fixie chainring, and all it did was tear the pants, and teach me to choose better what clothing I ride in.
There's no real harm to a chainguard, but not a lot of benefit either that I can see, so if you want one, go for it, but I'll be fine without. I'd say the lack of brakes is a far bigger hazard when riding on the road.