Actually, now that I am re-checking it seems that:
1. SQLyog doesn't use double quotes (“), it uses ` (correctly)
2. In my attempts at finding the problem, I mistakenly used ' instead of `
In fact, I got confused and this is actually a MySQL Administrator bug! The bug is valid, MySQL Administrator does use ” and the script doesn't work, but that's not a SQLyog bug, sorry …
I was trying to combine using MySQL Administrator for scheduled backups (until SQLyog implements scheduled backups), while using SQLyog for everything else (such as one-time backups or restores). Looks like for now I will have to edit the MySQLAdministrator scripts, or else use one-time backups done via SQLyog.