Just to make sure that there isn’t hard water scale buildup causing the problem, remove the skirt from the lower part of the APC. The stainless steel cylinder twists off, so you can clean the temperature probes, heating element and impeller. (be extra careful of that last one - it has a very thin shaft that is prone to bending).
When you inspect the components inside, they should be bare metal. If there’s a white-ish coating on them, that’s hard water scale. If it doesn’t rinse off with a blast from your kitchen faucet, then you want to soak it in a vinegar / water solution until it’s absorbed.
If there is no hard water scaling, was the water level between the min and max lines on the skirt?
Barring those two, I’d say, yes, this unscrupulous individual appears to have sold you their defective unit. I hope you used something like PayPal to protect yourself? Barring that, I would contact your local police - if you have any contact information for the individual (having a text conversation on your phone would be valuable for example) would help in tracking them down. I wouldn’t recommend letting the seller know in advance that you’re doing this.
When buying anything second-hand (eBay, Craigslist, Kijiji, etc) - you really need to be cagey, unfortunately. I wouldn’t buy anything from anyone unless I had real contact information for them (at least a cell number). And paying with PayPal gives you an out if they scammed you. (e-transfers may as well - check with your Bank if they offer buyer protection, that you can reverse an e-transfer if a seller has defrauded you of your money).
Don’t beat yourself up too much…most of us get taken at some point…lessons we all have to learn.