Given that that story, with that specific wording, has been a running joke circulating around the Internet for years, I suspect your co-worker's kid has never said any such thing.
The name “floppy” is itself a fossil as the entire device is rigid; in the 5.25” version the disk itself is still flexible but the envelope is inherently rigid due to geometry; only in the original 8” version was not only the disk flexible but the envelope, while stiffer, was trivially deformable by accident.
The disk is still soft in a 3.5" floppy. It's just in a hard case.
5.25" floppies had a much softer case. They would, for example, sag and bend under their own weight if you held one end, or bend due to air resistance if you waved them around. They didn't have rigid envelopes.
The device is rigid but the disk inside (note the device is a square, not a disk) is very much deformable. This can be verified by sliding the metal springdoor to the side and handling the floppy disk revealedd underneath
The meaning of the symbol outlives the technology that begat the symbol.