Only stupid people think a device that stores useful amounts of energy can be inherently "safe". Stupid people are dangerous! If you understand that energy storage has hazards, and take steps to understand and control those hazards, you can be perfectly safe.
Lithium Ion cells can burn or explode during the charging cycle or when shorted. This is simple fact, easily verified (don't breath the smoke!).
This is not normally a problem. In your laptop, the individual cells that make up the battery pack are connected with fusible links. These are basically very thin pieces of wire, that will melt at fairly low temperatures, that are glued to each Li-Ion cell.
When you are charging your battery pack, or if you foolishly short it out, the fusible links will melt before the Li-Ion cells have reached a high enough temperature to explode or burn. This will disconnect the cells from the power supply and/or short, so the battery pack will become instantly useless (instead of becoming a grenade or campfire).
If your lithium Ion battery pack in your laptop gets worse and worse for months or years and finally just won't hold a charge, it wore out normally. If one day it's just dead, with no warning at all, well your friend the fusible link probably saved your genitalia from laptop-induced cauterization.
The basic problem with this is that fusible links are not testable. You could test 99% of every batch, but you can't test the one in your laptop, because it's a one-use device like an explosive bolt.
But computer vendors have been very good about enforcing quality control on the Li-Ion packs they buy from battery vendors. If anyone's been hurt they've apparently been paid off handsomely, "Fight Club" style, and you can only see a few videos of spontaneously combusting laptops on the Intertubes. You're very unlikely to have your own mass-market laptop ever hurt you, basically because that's bad for business.
USPS has a different problem. Greedy bureaucrats cutting costs by hiring unskilled, ignorant monkeys to ship things. Gormless politicians creating workplaces that are dehumanizing and soul-destroying. The monkeys and dispirited humans who work in such places are quite likely to accidentally drive a metal object (think, forklift prong) deep into a pallet of Lithium Ion cells... and fusible links won't stop that short. And since it takes a while for a pallet of batteries to get into full blazing inferno mode, it could go unnoticed until well after the plane is off the runway.