That is an excellent observation, indeed, that I would gladly add to my structural reasons I just posted to the list. The generous (by US standards) unemployment and welfare system creates a powerful incentive for many people to register as "unemployed" even though they work under the table. I know of many such cases. The net result is that people who actually have jobs count as "unemployed" in Europe, in the US the same shadowy service sector jobs would count as "employment" because there is little incentive in claiming the "unemployed" status.
Of course the question is which of the two is more efficient and more desirable socially. The apologist of the US system would point that the welfare system undercuts work ethic and promotes cheating. There is probably some element of it.
However, the European welfare system can be thought of as "popular Keynesianism" i.e. government providing subsidies directly to the people instead of wealthy corporations. The benefit of such "direct benefit" from the Keynesian point of view is that they work better to stimulate demand - which is their intended purpose - as opposed to corporate subsidies which are often used to offset debts or losses or to finance mergers - whose effect on aggregate demand is minimal.
Wojtek