As an ex-academic type, your statement is both true and false. Some professors have large research grants, and indeed, their grants are what pay the salaries of grad students and post-docs.

Other professors (the vast majority) struggle to get appropriate funding. It's a horrible rat race to scrounge up enough money to continue your research. God forbid if you aren't tenured - your job literally depends on how much funding you can bring in (not enough papers = not enough funding = sacked for someone else).

That said, $25k is laughably small amount of money in research. At my old lab, I performed an experiment where I was easily blowing $1000 per week. And I was just a single technician in a lab. Hell, I spent more in supplies than I was paid in salary (probably by some multiple).