This is true, but that doesn’t mean that the department is wrong when they say MEng students are not considered for funding. I have absolutely seen departmental websites where the website says that MS students are simply not funded, or that MS or MEng students are only rarely funded. (Michigan and Cornell are two engineering MEng programs I’ve seen this language).
University research groups are sort of like small businesses, but they still do have to adhere to university policies. Faculty members can’t hire RAs who aren’t students, for example, if they have GRA funding that restricts them to that. There’s also such a thing as pressure - even though technically the grant may allow them to hire a master’s student into a GRA role, the custom in a specific department may be to only grant funds to doctoral students. The other thing is that faculty are motivated to hire students who are going to stick around for a while and get research done. It’s a better return on their investment to hire a PhD student who will be around 4-6 years than an MEng student who may be around for 1-2 (and has less of a motivation to do research in the first place).
I doubt faculty would leave en masse because they couldn’t offer funding to MEng students or if they were required to give preference to doctoral students. most of them would do that on their own.
OP, maybe it would be helpful if you would point to the language on the websites you’ve seen for clarification.