Advertising something as free and then charging for it is one of the most clearly unlawful marketing tactics there is.
No — advertising a certificate as free and then charging for it is a bait-and-switch, and it's unlawful under both federal and state consumer protection law. This isn't a grey area. The FTC Act's Section 5 prohibits unfair or deceptive trade practices generally, and the FTC has specifically identified misrepresentations about an education program's cost and terms as exactly the kind of conduct it enforces against — with real, multi-million dollar cases against schools that did this.
Most states also have their own deceptive trade practices statutes that cover the same conduct and that you, as an individual consumer, can invoke directly, separate from whatever the FTC chooses to do at the federal level.
The key legal question is usually simple: what did the school's actual advertising or written offer say, and can you show it? A clear written or advertised promise of "free" — in an email, a brochure, a website, an enrollment packet — is strong evidence, and the burden shifts to the school to explain the discrepancy once you can point to that promise.
If the "free" offer had clear, disclosed conditions you didn't meet — for example, free only if completed by a certain date, or free only for the first cohort of students, and that condition was genuinely and clearly stated upfront — then charging you after you fell outside those conditions isn't necessarily unlawful; it depends on whether the conditions were actually disclosed clearly at the time, not added retroactively. This is exactly why keeping the original offer in writing matters so much: it's the difference between a legitimate condition you simply didn't meet and an unlawful bait-and-switch.
Save proof of the original offer the moment you notice a discrepancy — screenshot it immediately, since marketing pages and promotional emails can be edited or disappear.