Or they could check if the source is open source and available on the internet, and if yes refuse to analyse it if the person who request the analysis isn't affiliated to the project.

That will still leave closed source software vulnerable, but I suspect it is somewhat rare for hackers to have the source of the thing they are targeting, when it is closed source.

How can they tell if the software is closed or open source?

They would have to maintain a server side hashmap of every open source file in existence

And it'd be trivial to spoof. Just change a few lines and now it doesn't know if it's closed or open