It follows, then, that in order for it to take more energy to produce the device than it will generate over its useful lifetime, the manufacturer would effectively need to spend twice as much on electricity as they sell the finished product for... And that ignores other overhead such as labor and raw materials.
Uh. Or they could just set the price above their total costs and still manage to sell them. Companies sell lots of things that make no sense, and successfully. Particularly in this case, people will obviously pay more for something "green" and their 'pay'ing price doesn't not have to have anything to do with the 'pay'back period.
Your overall point is still, of course, correct. This subject has been around long enough that even Googling finds some straight talk. The closest to the doom-and-gloom, "don't use solar power at all" articles and papers I could find were about heavy metal emissions, but even they put the ratio at 9:1 in favor of solar. http://www.livescience.com/environment/080227-solar-power-green.html
I did find one that clearly says solar may sometimes be bad for a bad install location (duh), and that solar is universally bad for gadget-scale use: http://www.lowtechmagazine.com/2008/03/the-ugly-side-o.html
In seeking the unattainable, simplicity only gets in the way. -- Epigrams in Programming, ACM SIGPLAN Sept. 1982