They always work on the first shot. When hunting, that's usually the one that counts. A bad shot, or a shot on a running animal has nothing to do with the reliability of the rifle.
Not saying the OP did either, but how many folks have short stroked a bolt gun, had an extraction problem with one, an ammo problem, a feed issue etc. ? They (Rem 750) are good guns for what they are, but they do have their peculiarities.
Like any rifle bolt gun or otherwise, you have to find ammo that it will reliably shoot and shoot it enough to have confidence in it. But you do have to keep the chamber clean. That's why they include a chamber brush with the rifle, and the owners manual specifically explains that.
I have a room full of bolt guns, some very nice ones. Sometimes though, I just grab that little short fast handling 750 Carbine and have a good time with it. Its ideal for what I bought it for, which is hunting in dense swampy areas.
It aint a BAR, or AR etc. Its a cheap semi auto hunting rifle. One shouldn't expect it to be anything other than that.
Could he have made the follow up shot with a bolt rifle, don't know. Again, not criticizing the OP, and don't know what the situation may have been.
I shot a deer last year (hit and wounded) that I tracked through three miles of swamp so thick that you could hardly stick your arm in it, in the dark full of briars, snakes, alligators, chiggers, mosquitoes, and ticks throughout the night . First shot was in a field at over 400 yards, right before dark with a $2,000.00 bolt rifle with a $2,700.00 scope on it.
That was my fault, bad decision. Nothing at all to do with the rifle.