Some guys are trying to argue that this isn't necessary, or that they've never seen this failure. I have, more than once. Seen this many times on BBC, big hp motors. Enough that many engine builders experienced with these motors, will take this extra step. Do you want to do it and be certain everything is right and you won't be tearing it out again for the same reason? Then tig it.
The housing is cast, and requires plenty of heat for penetration. The tube is stamped steel and can't take nearly as much heat. Tig is very isolated heat, and the best choice for this application. If you don't have time to do it right the first time, you're certainly not going to have time to do it again. It's very possible that once you tear it down, you'll find that the way it was fixed before, failed.