How do chemists verify certain phenomena like 1,2-hydride shifts, 1,2-methyl shifts and ring expansions?
I wanted to put this as a comment but I don't have enough rep :p

It happens the other way round, first the products are obtained, then the mechanism is proposed.

The point is, according to me that once it has been verified which product is major and which minor, chemists may try to come up with a suitable explanation for the product obtained, on paper. They may try some things, come up with possible mechanisms and sometimes even phenomena like hydride shift, methyl shift etc. Once they come up with such an explanation, they try to apply it to other related problems and upon reaching the right solution every time, they can say this is what might have happened to a high degree of certainty. 

So you see, chemistry is also sometimes glorified problem solving :p