I guess I'd side with your co-worker on the lack of veracity of the employment report. Most new "jobs" were created by the birth-death statistical model, not counted. The truer rate (if one were to count people who did not have a job but wanted one) would be just under 10%. Of course, it isn't actually possible to count every one, but careful sampling exercises have been conducted that lead to the 10% conclusion. I personally know people who gave up the job hunt and are outside the Labor Department models.
Are you aware of the Household Survey which a number of experts believe is a better predictor of the up rate? It always predicts a lower number than the Payroll survey. I would say that the current number errs on the up side. I’ve seen too many businesses advertising for workers in the last five years to believe that things are bad. Obviously some areas will be better than others. But people living in areas waiting for jobs to come to their area better be prepared to move to where the jobs are.
Do not get hung up on the number itself. The trend is the thing. Any model is based on conventions which might be arranged differently. The important thing is that the methodology be consistent over time -- and that occasional changes/updates be transparent -- so that trends can be observed.
People moving in or out of the labor force gets tricky. The issue arises frequently, for example, in trying to standardize international employment statistics. The assertion is commonly made (I'll leave it to those better versed in this area to give details) that the europeans park a lot of people in "training programs" that are really nothing more than disguised unemployment. Then there are the celebrated armies of 40 year old German "graduate students." Of course, the same might be said of a lot of the students marking time in college in the U.S. The OECD numbers are supposed to correct for differences in national statistical systems but I don't know how well they actually do so.
Discouraged workers who have left the workforce and are no longer counted as unemployed are certainly an issue. Those people, however, are still eating. They've found a way to put food on the table. A lot of "unemployment" is fairly discretionary: e.g., teenagers; spouses of an employed person who may or may not be interested in a supplemental income depending on their attitude this week; and semi-retired or retired people who may be thinking about returning to work. Then there's the underground economy, which is probably at least 10% of U.S. GDP (and higher in most of Europe because of the tax wedge).
No one model perfectly captures the complexities. The trend is the thing.