Johnson & Johnson v American Red Cross
Thus, on the merits, this appears to be a pretty clear-cut victory for J&J, subject to two important caveats. First, the adverse publicity from this suit---a bit like suing Santa Claus---could do more harm to J&J than the use of its mark would. Second, there's a chance that J&J could lose its mark entirely. Although I haven't done any serious research into the matter, my initial reaction is that if I were defending the ARC, I'd challenge the validity of J&J's mark either on the grounds that it has lost its distinctiveness, or that J&J shouldn't have been able to use the red cross back in 1887. As the J&J press release notes, that was before the formation of the ARC, but it was AFTER the 1864 Geneva Convention declaring ambulances and military hospitals neutrals, and designating the red cross as their symbol. Even if we assume that the Lanham Act takes priority over the U.S. ratification of the treaty, the prior use could void the mark under the Lanham Act (although perhaps it's too late for the ARC to make this argument).
The ARC could even argue that the red cross is not trademarkable because it is very nearly the flag of Switzerland. (The Lanham Act forbids trademark protection for foreign flags.) This argument is unlikely to succeed, however, because the Swiss flag is a white cross on a red background rather than vice versa. ARC would have to argue that the disqualification for national flags contains an implicit corollary applicable to dyslexics.
My suspicion, however, is that J&J will win, in large part because the ARC press release doesn't make any good arguments on the merits. It simply accuses J&J of being a greedy company. Presumably, if the ARC's lawyers thought they had a good response on the merits, they would have mentioned it. Thus, I'm led to conclude that my own arguments above are probably lousy ones.
Either that, or ARC's lawyers did not have anything to do with the press release.