"A region zero DVD will play in any DVD player."
...well... ahh... yes and no... an American or Hong Kong "Region 0" DVD (which is encoded NTSC) will indeed play on a R1 player - but a European with a R2 player that has not been 'chipped' will only see a black-and-white image on his display...
"Region 0" has nothing to do with whether a DVD is 'legit' or not - R0 (a.k.a. "All Region", a.k.a. "Region ALL") simply means that the disc has not been coded for any particular Region. Most (American) CRITERION DVDs are "Region 0", so are many (American) IMAGE DVDs, and (probably) all 'adult' DVDs regardless of where they come from...
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If a DVD is a new title from a major studio and it says Region 0 it is almost sure to be bootleg. Some websites offer such DVDs and designate as Region 0.
Make sure it's the right format. I have an Austrailian region 0 DVD (Midnight Oil) and it is PAL. If your system can't handle PAL then they won't work.