I was under that impression as well. Hard to know what to make of all of the Amazon customer images of LiFePO4 batteries which caught on fire when they're not supposed to be able to.
https://www.amazon.com/Battery-Tende...70_&dpSrc=srch
Edit: my electrical theory is a bit weak but isn't it the case that since capacitors self-discharge, leaving one connected to the battery all the time would eventually drain it?