At a tough spot career-wise... not sure what to do

Yes, they are lying. People selling school programs are working to get butts in seats, which makes THEIR job secure. They don't give a damn about you, nor do they care about employers in the community. If they did, they would be proactive in interacting with industry and placing their students. They would be someone that actually cares about what they do, and the people they interact with.

How much machinists training was involved in your BSME? Have you considered hitting up union halls? Apprenticeship, then journeyman. It makes good money, save as much as you can. Once you have that experience, plus your degree, you'll have a pretty hefty resume. That's if you even want to work for someone else after gaining that experience... There is nothing wrong with blue collar work.

Also, remember that a lot of finding a job still boils down to who knows you. Patronage, nepotism whatever you want to call it. It is real, it sucks. To combat that you may want to just hit the pavement and sell yourself to businesses. Cold call them. Do not leave until they tell you NO three times. Tell them that you'd like to intern for them and show them your work and work ethic. Your work ethic is what will get you remembered. If they do not notice it, then they are not worth working for.