I spent some time this morning trying to work this one out but it was a simple solution in the end.
What was confusing me was that I could view the source of my CFML file in Firefox...
...and when I clicked on the script links, I could access the corresponding code...

Yet somehow the Javascript wasn't working.
The solution was simple - although the CFIDE virtual directory was mapped correctly in Coldfusion Administrator...

...there was not an equivalent in IIS.
I added the virtual directory to IIS and now Bob is my proverbial uncle - cfajaximport works just fine.
I'm not an expert on Apache/Tomcat etc but I suspect the same issue crops up on that platform and can be fixed similarly easily.