If 'open source' isn't about having.... I dunno, all your source-code being licensed under an OSS license... then what exactly is it?

I think the word you're having more of an issue with isn't 'open source', but defining what exactly a 'project' is vs. a business. On that latter point, I would agree with you that a project doesn't seem as much of a 'project' when most of the core people are employed to work on it towards specific goals the funders have designated.

That's how most projects work. This one just isn't a hobby.

"They are no longer true open source projects."

As long as the source is open under a permissive licence they are open source.

If someone has figured out a way to make a profit model around it - I would say, that is a bonus as it entails support for a long time and guarantees end-user-valuable goals driving the project.

When was the last time government was responsible for distributing something fairly?

I think the consumers of the open source software must be responsible to ensure financial health of those projects and not tax payers. Simply because in such cases more useful projects would thrive where as bad projects would die out quickly.

The last thing I want to hear is that Mozila called Bill Clinton for a lecture paid him $1M and later Hillary gave a grant of $100M of my money to Mozilla. That is how governments works.

That sounds a bit like a No True Scotsman argument there...

There are clear criteria for what constitutes open source. Perhaps, 'indie projects' would better capture the feeling you're trying to express.