I do not recall reading anything, but my memory is mush, that proves that nobody returned to work. Its more that in total there was not an improvement in employment, but I could not swear that nobody fit that description. If one person did get into work, and three dropped out of work, for example, the average would be worse but there would indeed be one who returned to work. It would be more desirable to say, instead, that given that the numbers show no improvement in employment its possible that nobody in the study returned to employment.
Arguing that the economy was to blame is taking people for fools. Sure, of all those "recovered" many might not have been able to find work, but all of them, or even most of them? Its very unlikely. Again, this is persuasive rhetoric instead of evidence and reason. Its a lot like "the dog ate my homework".
Of course if nobody or nearly none of them really recovered then its no surprise there was no improvement in employment. The recovery threshold was, after all, in the range of the typical 80 year old based on SF36PF.