This behavior is why so many house fires are blamed on electrical.... uh, I don't know what happened sir, the wall just spontaneously combusted.....
Let me know how many house fires you have personally seen caused by somebody welding in the garage please.
My understanding was its the 8 outlet ports in the kitchen made of cheap plastic that catch fire. When people are welding they are generally aware that things can catch fire and try to pay careful attention. Welders just need to be more responsible is what you are telling me. My experience is that this is pretty much ALWAYS the case as well, people who work on their own stuff tend to be more responsible about these types of things as well.
Again, I restate, if it were me, I would inform the owner I would be working on my vehicle in the garage and doing some welding. I wouldnt be asking permission. That is what home owner's insurance is all about, also why the owner takes a deposit, also why renter's insurance exists. If something goes wrong you make good on it one way or another.
You can approach the problem any way you like, but if done the right way both the owner and the renter can be happy. Its all about communicating the need and getting them on your side.
Or if you prefer you can look at everyone as the devil and merely exist to screw you. But I much prefer to look as everyone as honest and willing to help. There are quite a few crooks out there, but I prefer not to burn bridges if I don't have to even with crooks.