Even if it were closed-source, technically there's nothing stopping you from binary patching your browser to do the same thing. But then again, there's nothing stopping you from putting an ad-blocker in your normal browser; and faking clicks on your own website to "milk" advertisers is already a thing that has to be dealt with.
I don't think either Brave's model, or its being open-source fundamentally changes the issues facing ad-supported systems.