Although anti-poaching agreements could certainly be used to the detriment of employees seeking to further their careers by changing employers, I believe the original reason for such agreements was to prevent one company from interfering with the development plans of another. For example, if Google were to make a significantly above-market offer to the top 20 engineers working on OS X 10.7, it could delay Lion's release by months or even years. If a larger company, like Apple, wanted to put a smaller company permanently out of business, it would just have to make above-market offer to all of the other company's employees.
Then the solution to that is to have longer term contracts with options on both sides.
Many industries make use of contracts that specify a minimum time period (say 2 years) with the additional condition (in legal terms, technically a duty) that a particular project be completed. If someone is so vital to your project, you would be a fool not to incentivize them to stay.
You are a criminal if you break the law to keep them there.
I have a feeling that this case goes beyond short term projects, though. I'm sure that since top talent typically works on multiple projects at the same time, it would have been hard to go long without a contract renewal. The companies thus had the "brilliant" idea to simply fix the market for an extended period, greatly benefiting them in negotiations.
With respect to this case, would the plaintiffs not have to prove that they were not hired for positions for which they were the most qualified candidates?
They only have to prove it beyond a preponderance of the evidence, though, not beyond reasonable doubt (the standard for a criminal case). As long as it's more likely than not that the companies colluded to prevent worker mobility, the companies will lose.
However, don't think for a moment that this case is actually going to end up before a jury. The discovery process and evidence introduced at such a trial would be ruinous for all of these companies. I would bet that they would much rather settle it now and avoid the bad publicity and legal expense.