Which is called passing off and is illegal.
On what basis?
The board could be confiscated by customs.
A lot of stuff can be coonfiscated by customs, sometimes wrongly.
the FCC and other approval
I find this quite interesting. Why did the arduino team think it was necessary to be certified for CE/FCC? and under what rules was the arduino certified? Unlike (all?) FCC certification I have seen, the arduino board has just a fcc logo and no cert number. I suspect that it is part 15. But many such emitters (broadcast radio for example) don't have part 15 cert. And earlier arduino boards had no fcc cert of any kind (at least they didn't show any). So if the arduino team thought that it was legally required to have the cert now, it must be the case that they thought those earlier boards are illegal in the US.
Anyway, with or without the cert, it doesn't bother me.