I think the Apple rep might have been referring to the "swelling" of MacBook Pro batteries kept constantly at full charge.
In the past, batteries were NiCAD or NiMH. Those batteries, when left on a charger that didn't shut off automatically, would "burn out". I remember that being a big deal with old generation laptops from 10+ years ago.
Newer notebooks will use Lithium Ion and not have that issue. The Apple site confirms this: https://www.apple.com/batteries/why-lithium-ion/ Modern devices usually use an hard case Li-Io battery. Those batteries are very durable and don't explode (unless you really abuse it).
MacBook Pros and most smartphones, though, use a different type of Li-Io battery. Often called a Li-Po (Lithium Polymer) battery. This is Lithium-Ion gel inside a plastic bag. This gel is around 20% more efficient than traditional Li-Io batteries, can be squished more easily into tight spaces and is lighter. The problem is Li-Po batteries swell when at high charge levels (ever noticed your laptop heats up around the power connection while charging?). Smartphone batteries are small. The MacBook Pro's battery is big (relatively). That leads to more swell. Assuming your charger is working correctly, the charger cuts power to the battery near 100% and then tries to keep it at that high level. Always being near full can lead to the battery rupturing as they age and can accelerate that aging process.