Marie, Stop worying it will probably never happen. Airlines base their immoral practice on statistics that indicate how many 'no shows' there is likely to be. It is only when these guesstimates are wrong that folks get bumped. And yes, even with a boarding Card in your hot little hand you can get bumped right at the gate.
You can retaliate and protect yourself by trying to use EU flagged Carriers who are legally obliged to pay significant compensation to bumped pax. Mainly in Europe naturally but it does cover flights to the USA.
But as I say, it is not likely to happen. Getting to the airport early having booked On Line reduces, but does not entirely remove, the risk.
They must ask for volunteers first and it is only when no one volunteers to take the offer that involuntary denial takes place. In all my time flying I have never been denied boarding. I was once asked to volunteer, for a nice deal, but could not (and ended up getting bumped but up to First, not off the plane.)and another time I did stick my hand up and took the money, €400 EACH, a night in a fancy Hotel, as the plane was running very late anyway.