Before Unicode, 'μ' was typically entered as an 'm' in a Greek font. This can go wrong in several ways, like if you converted the document to plain text, or if your laser printer didn't have the font and it substituted a regular font, you're suddenly off by a factor of 1000. 'mc' is ugly but safe.
What time period, system and region are we talking about? For some characters using a specific font was certainly necessary but for µ? It is in the original IBM PC character set from 1981 and could easily be put into plain text files. I would guess that most extended ASCII character sets contain it but I don't know for sure. Every [German] keyboard I ever used had it on the M key.
I remember having to get a µ that way using FrameMaker on SunOS 4 in the mid-90s.
Mac had a µ from the beginning. And some PC code pages did. But PCs in Canada (where I'm from) used code page 850, which had an Á (for French) where µ would be. Just the sort of thing that would hose you if you tried printing a Mac document on a school printer.
Is that some joke about medical writing?
Anyway, I just noticed that table doesn't have rules for nanogram. There is also no mega-anything.
(On a serious parenthesis, I think I actually understand their rationale; but changing the abbreviation of only one of them is still confusing.)