To be fair, the simple phrase "stay alert" doesn't tell us anything.
I had a look on the TAAT on that and someone had posted a graphic with a bit more information, which basically boiled down to "keep socially distancing, and if you spot any symptoms then self-isolate" - which is really not what "alert" means. The only part of that which "alert" could possibly relate to is "notice if you have any symptoms".
I think a lot of the people questioning the phrase aren't confused or stupid, the're simply irate at the sloppy use of language (I know I am).