When the PICAXE is reset, its internals are initialised to default setting, and the first job of the Firmware is to to adjust internal settings to what they must be for normal operation. Therefore the PICAXE shouldn't get locked into any mode other than its default of 4MHz operation. In the worse case, it would be necessary to power off the PICAXE and turn it back on to force a hard power-on reset. On an 18-series, pulling the Reset/MCLR input low should do the same, but it is possible that the PICAXE handles this event differently to a power-cycling.
The caveat from Tehnical may be more precautionary than anything else, and I've had no such problem when I've experimented with under-clocking. Providing you are prepared to accept such a risk associated with underclocking ( a very minimal risk, IMHO ), you shouldn't have any problem.
Most manufacturers have to protect themselves from users doing things with their products which they aren't designed for and then complaining and demanding replacements if something consequently breaks, so such caveats are common place. I cite such caveats when I know of them, so I don't blamed either if it goes wrong