It seems that in chess, the (current) "best" way to figure out whether a move was legal is through retrograde analysis (1). As you can imagine, this becomes very expensive, very fast. Not only that, but the current position may be legal in chess given some previous conditions, but illegal given others (consider Castling). Therefore, given no extra information, you may not be able to tell whether a given chessboard is legal without being given the entire history of the board as well.
Disclaimer: I don't know what I'm talking about, just googled retrograde analysis
Right. So unattainable means "not feasible", not impossible - or that it's not possible to enumerate all legal positions. I of course realize that simulating all possible games (ignoring cycles) would be very demanding.
I'm not sure what ruleset OP is using for their analysis, but with superko in place you would also need the entire history of the board to know if a move is valid.
Although rulesets might differ on what is considered a legal move, they all agree on what is a legal position: one where every connected group of stones has liberties (empty adjacent point). Furthermore, in all rulesets you can reach any legal position by playing legal moves (and passes) from the empty starting position.
Disclaimer: I don't know what I'm talking about, just googled retrograde analysis
1. http://en.wikipedia.org/wiki/Retrograde_analysis