Not only do they allow it, they actively encourage it. They tell businesses that it's really important to buy ad space on searches for your own brand name so that a competitor doesn't.
The way they say it really comes off like a protection racket. "Nice number one spot for searches for your brand name you have there, would be a shame if anything were to happen to it."
They make people feel better about it by giving a steep discount over normal ads, but that doesn't make it less of a racket.
Experienced this as someone doing ads for SMBs. The Google advisers call and after messing up the configs for your campaign (to your disadvantage that is) they advise you to include your brand name as keyword. No matter that 3 out 3 Top results are already for your company.
I don't think that someone could actually use your brand name and get away with it long-term (though, short-term, as the original post evidences, isn't guaranteed) but a competitor can absolutely buy ad space trying to steal your customers.
Like, if you search for "Nike" and Nike hasn't bought the branded ad space, you might get an ad for Adidas as the top result, with Nike's homepage the fourth item in the list.
The way they say it really comes off like a protection racket. "Nice number one spot for searches for your brand name you have there, would be a shame if anything were to happen to it."
They make people feel better about it by giving a steep discount over normal ads, but that doesn't make it less of a racket.