An unmodifiable system will never satisfy the requirement, a modifiable system will.
There is no passus in either the LGPL or the GPL that says it has to be easy.
If you want to modify any Free Software program on a Linux Live CD, you have to copy the software from CD to modifiable media, apply your changes, remaster the CD image and burn that new image.
Modifying an OS image and reflashing a device is no different.
"It doesn't matter whether we call that "embedded" or not"
Indeed. Embedded does not imply unmodifiable or vice versa. Hence my objection to the original statement. Neither embedded nor mobile devices are by definition unmodifiable.