Re: Are they right?
You're going to see the Max Power Draw (usually) mid-way through the Windows loading screen. When you initially turn it on and it goes through POST, it doesn't power everything on at the same time at full draw. When Windows starts booting, loading drivers, starting services, that's typically where you see the what your system should run at. Now, this obviously is not correct for newer systems, as every resource might not be needed at max to launch Windows quickly. You could need a higher PSU, but I highly doubt the manufacturer would bulk produce a PC that would fail. That just costs them money in labor. You only the S&H charge, but they are paying people 10-30 (Euro/Dollars) to fix those things.
They are getting their information from the Parts manufacturers. You can google your parts and find how much power they require at max. It should be listed under the specs as "Max TDP". They may have two numbers listed on other parts (e.g. 45w/65w) which just represents the minimum running requirement and the maximum needed.
As for labor on the original request. Ask for a supervisor, explain the entire situation, be polite, do not threaten, beg, say how unhappy you are, just be honest about the facts. You sent it in when it wouldn't start, they sent it back saying it was okay. It failed again and they discovered the problem. It's not like you wanted to lose your new computer for a few days/weeks, pay shipping, just to give them something to do. The company can prove they found nothing wrong the first time. Therefore, they can prove they owe you nothing. Crappy, but that's how it goes with a large business.
Humans are the only creatures that won't live up to the their potential. Give everything your all. When you die, die on E.
So I ask you, what do you intend to do now?