Tried multiple cars, same thing. So there must be something wrong with the solo. Anyone else had this?
I follow, and support, your troubleshooting to date.....but I'm here to tell ya that it doesn't prove there's something wrong with the Solo. In fact, just the opposite?
If it charges with 12 VDC from the wall wort (charger) but not from the 12 VDC from the car cord(s)........how does it know where the 12 Volts is coming from? Volts is Volts. Since the charger works (obviously by providing the 12 VDC expected) the Solo the Solo is fine.
Without a trusty meter to sniff out the voltage you're up against it WRT traditional troubleshooting I think. You're out of 'known good' parts and don't really have a working system to substitute from. I suggest "the Columbus Method". You know 'stumble on it and claim you got there on purpose'?
Check the cords for fuses. It's nothing fancy, two connectors, some wire and maybe a fuse. Hard to say how you might blow them both, but I've had new cords without fuses as well as ones ridiculously under or over size. Suspect the car jacks (key not being on, poor center contact being common faults). And so on.
A meter would sort it out in seconds of course, but has to be there to do so. I realize this defies the 'but it happens with both cords and different cars' idea, but the idea that it's a fault with the Solo is not holding any water with me right now. FWIW.
To answer your question, no. While others have had problems with car cords nobody reported one that was the Solo at fault in the situation you describe.
Good luck with it, please let us know how it shakes out? TIA.
OF