Many media have special requirements for writing. It's true that DRAM and SRAM don't have a separate "erased" state, and neither do fuse PROM, core memory, Williams tubes, acoustic delay lines, or magnetic disk and tape.
But CD-R, Flash, CD-RW, rewritable magneto-optical disks, two-photon storage, and some other memory types have a distinct "erased" state; in some cases, you can't even return to that state. I'm not sure about MRAM, FeRAM, PRAM, and hypothetical memristive memories.
Whether this erase procedure happens immediately upon the user's request to delete the information or whether it's added to a queue of areas to erase (the "purging routines" or "garbage collection" mentioned in the article) is a small detail. A modern OS will return control to the user immediately upon issuing the command, and all that matters to the end user is that the erase command is issued before the next write. A firmware
I seriously hope that these researchers aren't advocating a mandate that states that the erase procedure cannot be issued until a write is requested to that space.
In any case, I still think your point is valid despite disagreeing with you, and I think it's disappointing that you just received a downmod. I've just upvoted you back to 1.
In NAND flash, overwriting isn't even an option, although I don't understand why.
Flash is the unusual case since it needs to be "flashed" in bulk before it can be rewritten.