Miraculously, it worked... so not only are the PICAXEs programmable by DIYers like me, they are idiot-proof as well!
Although it may work now, it may fail "inexplicably" down the road and it may also sometimes do weird things as a result of internal damage. When I have experienced these weird conditions I have spent many hours trying to figure out what is going on, only to come to the conclusion that there is something wrong with the chip and then remembering the inverse insertion. Replacing the IC after an event like tihis is always a good idea- it will pay for itself in the long run.
Thanks Aubrey, yes I was very lucky and it may not last. I am powering my kit from 3 x AA batteries and the batteries I am using are not the best. I think that is why I got away with this. If I'd had it on a 5V 1A supply it would have been toast I think. Anyway a new chip is a few dollars and the code is open source and all chips on Picaxe's worn boards are socketed, so easily fixed. I have a few LCD Dislplays with a 2x7pin ribbon cable header, so I could easily make up some PCBs myself for them to use this one wire system.
@Max - it is good advice and I have in part taken it - I ordered another one-wire display board only to go with another of my displays - I have tons of LCDs and a couple of monster (think 9 x 5 inches) vacuum fluorescent 4-line x 20-char displays I got on a sale at one of my suppliers. But it will also be a spare. The chip is socketed (as are all Picaxe board chips) so easy to swap.
There's another very good bit of advice I once got - if it works, don't fix it! Since this is not a commercial product going out to a customer after repair, I'll go with that one for now!