Do people really counter with salaries that are 50% higher than the initial offer? Maybe it is just the nature of the employers I have dealt with in the past, but I have always felt anything in excess of the 5% - 10% range just meant that you and the company were too far off in expectations for a deal to work. In fact, a few months ago I rejected a seriously lowball offer where the difference was similar to the numbers you posted; I didn't even bother to counter. Is it really common to get companies to move by double-digit percentages on initial offers?
Edit: I should point out that people at this company had already told me how hard it was to find qualified people. There were plenty of other indications that they could not afford to be throwing away candidates.