Penicillin needs to be given slowly in whatever muscle you choose. Most use the neck because horses do not like the sting and when you use the butt, they can kick.. So the neck is easier to reach with less chance of getting kicked. It still needs to go in slowly, the faster the injection, the more it stings.
K-Pen( I think its called) can be given in the vein, but it still has to be done very very slowly to watch for reaction, and is usually only done by vets.
Penicillin can and has been used to euthanize horses in extreme conditions when nothing else is available. And I hate to say it, but the explanation given by the OP is not what happens when Pennicillin goes into the vein, the horse immediately collapses and can have seizures, but they do not get up again. It takes awhile to actually die with Penicillan, it is slow. When people would want to euthanize a horse but not have personal property and had to take to dump to dispose of, we would give a light tranquilizer first, then lightly sedated inject the Pen. Horse would drop but heart still beats for a bit, some leg "seizures", not the calm way of the usual euthanisia. The dump requires with a bullet or Pen injection, no buthanasia injection in case of burial at dump and ground contamination.
I am sorry for the death of this horse, but it sounds more like the horse reacted to the sting and went over and out of control. Two lessons: always carry a gun when camping or out of fast phone contact and when giving pennicillin, be very careful of how its administered and where.
Uniprim is one powdered Pennicillin and is great, one or two scoops one time daily in grain or mixed up with applesauce by mouth, no shots. Its amazing how many people say after giving Pennicillin shots twice a day for the treatment, their horse is alot more spooky and weird when approached. Those shots HURT and STING and horses hate it.