In my previous company, as it was reaching the end of its life (I was becoming burned out on the idea and the business) I made dramatic price changes over the span of a couple of years. I increased the prices by about 50% every six months, and made minor tweaks to the model lineup to make them more profitable even without the price changes. The result was generally happier, but more demanding, customers. As tptacek mentioned, it was a filter...we got a different
kind of customer with the price changes. They were less educated about our products, Linux, and technology in general, but were more enthusiastic about the benefits we provided for them, especially our unlimited technical support. We also made more money; sales volume didn't decline remarkably, but the revenue per unit sold went up. Nonetheless, the hours I had to put in to support those units increased. If I had kept that business running I would have needed to raise prices even more or stop offering unlimited support (making support a paid for option has always seemed somehow wrong, to me, but it works for many enterprise companies).
With Virtualmin, we started out charging 50% the price we knew (and everybody else also knew; it was listed as being "on sale") we would eventually charge. I did find that the number of customers demanding even lower prices dropped to almost nothing when the 50% off discount ended. Those customers simply weren't in our market segment, and went back to second-tier products that cost dramatically less and offer dramatically less capability. And, I suspect, but don't know for sure, that cPanel and Plesk customers became more likely to migrate to Virtualmin after the price increase. But, I believe that has more to do with perception of value in an existing market with existing price expectations, rather than any particular price point.
Anyway, I believe the rule of thumb is roughly true. Cheaper products certainly attract a buyer that has weaker loyalties (as soon as they find a better price, they're gone). They probably are also more demanding.
We have a range of prices from $138 to $998, and I would wager that the $138 buyers are at least twice as likely to ask for support as the $998 buyers. I don't know how to make that more fair for us or the $998 buyer, however, since the pricing is based on usage, and a natural result of using the product more is being more familiar.
The point of all this rambling is that I don't think there are any hard and fast rules, but I do think charging more is worth an experiment for most companies. You can always revert your prices (and refund the "suckers" who bought at the higher prices) if things go badly. At worst, you'll learn that lower prices were a better position for you.