It really depends upon what we mean by "oil light". Some cars (GMs particularly come to mind that I know for sure, but there may be others) have a light for "low oil level". If that were to come on, it really wouldn't be that big of a deal because I'm sure it comes on well before any damage could occur. Likewise, there are many cars that have a "maintenance interval" or similar light, and that one is just based on a mileage interval on many cars. Some more sophisticated ones use several different computer inputs to come up with that interval, but still not talking damage here.

Now, if the low oil pressure light were to come on, this being the real honest-to-goodness actual oil warning light, and you drove more than a couple miles (or even much more than pulling over to the side of the road in some cases), the engine probably would be shot. It would depend a lot on what was causing the low pressure, and how low it actually got (in some cars there may still be a gauge, but in many there isn't), but this is the serious problem light that really shouldn't be ignored.

The thing is, in a rental, how the heck do you know which is which? It's one thing to know the distinction in your personal car which you drive all the time and have taken the time to know the details of its operation. Most people renting aren't going to know. I'd probably fall in the middle there: I might stop and try to make sure which warning it was trying to give me, if it wasn't readily apparent.