You are probably correct. Sometime in the late 1980s, I worked out that "law-abiding" was not the opposite of "random" (reading lists of odd laws, they seem to occasionally be synonymous). For the law/chaos axis to make sense the two need to be opposites. The only thing that made sense to me was to have Law refer to those who tended to think/act in terms of groups and for Chaotics to think/act in terms of individuals.
If I had to define the alignments, I'd do it this way:
Lawful Good -- believes the most good can be obtained by maximizing structure/order and that the good of the whole will always outweight the good of, or cost to, the individual.
Chaotic Good -- believes the most good comes from maximizing the freedom for each individual to act of their own will. Good cannot be measured in a group, but only to each individual.
Neutral Good -- Seeks good through a blending of both methods, unwilling to move too far in either direction.
Lawful Evil -- believes that the greatest personal benefit can be obtained by enforcing order, of a sort, upon his surroundings. The sufferings of others, as a group or individual, are irrelivant, so long as he personally profits.
Chaotic Evil -- believes that the greatest personal benefit can be obtained by using personal means and reacting to each person or situation independantly of other encounters. The sufferings of others, as a group or individual, are irrelivant, so long as he personally profits.
Neutral Evil -- Seeks personal gain through a middle ground of the two methods, using some basic order, while dealing with some circumstances separately. The sufferings of others, as a group or individual, are irrelivant, so long as he personally profits.
Lawful Neutral -- Finds confort in order and group cohesion. The impact of that order is not measured against woe or weal.
Chaotic Neutral -- Enjoys personal freedom with neither concern for, nor malice toward others.
Neutral -- Seeks benefit for self and friends, without overmuch concern for others, but with desire to harm others. Finds order comforting, but does not want to be overly regulated.