I have never heard of that inspection rule either.
What I do know is that it is no longer a mere sumonnable offence if you are caught driving with an expired road tax.
Previously, if you are caught, you get the option of just paying the fine, or, you challenge the summons by appearing in Court.
Now you no longer get the option of just paying the fine. You actually have to present yourself in Court before a Magistrate, pay your fine, and possibly get demerited. A colleague just went through the experience. They are now taking it very seriously because they consider anyone with an expired road tax to be without proper insurance coverage.
So get your road tax renewed a.s.a.p. As far as I know, there is no time-limit inspection rule.