In addition to the perfectly accurate answer given elsewhere, it may also be useful to consider the lower level meanings of the phrases dominant and recessive. In both CAN and LIN at the physical layer the bus "floats" to a particular state when no nodes are communicating. This is the recessive state. Any node which drives a dominant bit will override this state (hence the word "dominant").
This is used within the protocol to allow non-destructive arbitration to occur, where the node with the lowest id "wins". This is due to the decision to signify a logic low by a dominant bit.
(The standards could have been written the other way around. There's nothing that demands a dominant bit is interpreted as a zero in any other context.)