I'll start by saying that the trouble with my tires was the only mechanical trouble we had during the whole journey. That is to say, over 30 days of two guys covering 2,000 miles (so, 4000 man-miles), and crossing a couple of eco-systems, we didn't experience so much as a single flat tire. No twisted chains, no missed shifts, no annoying rattles or creaks dogging our progress. Whatever problems we had began and ended with our own legs and lungs.
Now, it's certainly true that our happy travels owed a significant debt to luck, but that's most of the benefit of adhering to the importance of the new. When my tires went, they went thanks to bad luck. The sidewall cut, well, who knows? Perhaps a sharp piece of metal on a bike rack somewhere. Perhaps a piece of glass in the road. Either way, just luck (or lack thereof.) To an even greater degree of chance, the complete dissolution of the back tire is probably something that even the scientists at Specialized didn't see coming.
The nice thing about bad luck is that it doesn't really lend itself to engendering hard feelings. If I had been some asshole that derailed the trip thanks to my laziness or penny-pinching ways, my companions probably wouldn't have been so game to help me source new tires in tiny towns. Worse, if lethargy or miserliness led to a truly progress-ending event like a seized hub or a broken chain, would it not have been fair to leave me to my fate? Perfectly fair, I'm afraid, especially because we were working on a fairly tight timeline.
It's for that reason that Tando and I both opened up our wallets and paid out for new everything--it's a courtesy prevents putting your friend in the position of choosing between finishing their tour on schedule and sticking with you. As an added bonus, that pay out makes it all the more unlikely that you'll be faced with that choice at all, or even have to deal with some greasy headache or other on the side of the road. All those new parts aren't just shiny, they're insurance.