What it comes down to, is that its foolish to rely on a business that lives entirely in someone else's garden... if google play just shut down tomorrow (i know, not likely, but you never know with the way patent trolls are these days) then you'd be just as screwed... if you base your livelihood on a business you own that is in and of itself reliant on a third party, you're not going to have much stability.
There are a lot of businesses based on iOS/Mac app stores, Play Store, Amazon's EC2 infrastructure, Amazon's seller marketplace, eBay/PayPal, reselling (e.g. domains, hosting, etc), which won't meet your criteria.
Now let's look at non-digital goods: All new car dealerships, every shop in rental space (which is almost all of them), all airlines, in fact all airport-located businesses, government contractors, all franchises, et al.
So what businesses exist which aren't reliant on a third party? If we ignore government as a "third party," there still aren't very many. Most businesses rely in some part or a large part on a third party.