What the Lenovo rep told you is, as much as it might surprise you, quite valid. Each battery has a communications controller in it, which is how the laptop (and software on the laptop) can tell what it's capacity and charge percentage is, battery manufacturer/brand, blah blah. It's very possible that either the chip in the battery, or the chip in your laptop could be bad. If you've tried multiple batteries and the behaviour is the same, then I'm inclined to think the faulty part may be in your laptop.
This certainly sounds like a hardware-level issue and not a software issue.
Bottom line: make this Lenovo's problem. They are the only ones who can help resolve a hardware issue of this nature.--
Making life hard for others since 1977.
I speak for myself and not my employer/affiliates of my employer.