Cells/packs used in these hobby applications typically lack an outer protective shell, and are of the pouch cell type. This makes them more susceptible to damage, but is done for primarily weight considerations likely. Typical notebook or phone batteries will be encased in some form of structure that protects them, and for smaller batteries, like in phones, can prevent the fire from exiting the enclosure to some extent.
Furthermore, these cells/packs are designed for shockingly high instantaneous discharge rates, which means that any accidental release in energy will be correspondingly fast and violent. It seems that protection of the battery is the charger/device's responsibility, so it's also easy to accidentally use batteries which have been overtemped/overdischarged/underdischarged/overcharged. (they also have much lower design cycle counts than typical electronics batteries). Typical electronics batteries have a chip in them that will disconnect the battery, sometimes permanently, should any of these conditions occur at some point in the battery's lifespan.
I would personally recommend against the storage or charging of such batteries indoors without measures to contain any potential fire. For what it's worth, discharging (and maintaining) the batteries at a low state of charge will also decrease the amount of energy available for combustion.