You're missing a couple of points:
1. That's income. What about expenses like taxes? These have increases substantially, leaving less disposable income.
2. What about the cost of getting that job? If you need to go into debt to the tune of tens of thousands of dollars befor taking your first job, then what is the net result on total income? What if you could take $100K and invest it in a mutual fund when you were 18 and then add that on to your salary because you didn't waste it buying a certificate of work eligibility from our educational institutions? That would be the equivalent of the situation in 1965.
3. This is the average, not the median. Because we have already noted that the rich got a lot richer, that means that if the average stayed the same, then the median person went backwards. Also we know that disproportionate income was dedicated to women and minorities. That means that the average white guy supporting his family is much much worse off than he was in 1965.
4. Why brag about being stagnant? A growth rate of 0.2% during a time of tremendous economic productivity means that the average worker has not been able to benefit from the computer revolution, as well as all the other benefits of an entire generation of economic growth. This is in stark contrast to prior generations when the average American's standard of living rose enormously.
No, it doesn't mean that at all, and you haven't even phrased it correctly (the average went up .2% per year in even the very worst selected period in our data - that's NOT staying at the same wage).
2 million rich people can get richer at 4% each year, while 280 million people get richer at .1% each year, but that doesn't mean that the median income went backwards.
What it means is that the median income went up at least .1% each year while the average income went up .2%.