I think the law is very clear in that the reproduction and distribution of copyrighted material without licence from the copyright holders is considered an infringing act. It is also illegal (i.e., the commission thereof constitutes an offence) in certain circumstances.
If Odex is the exclusive licensee of the anime titles, it may bring an action against persons who have allegedly downloaded titles to which it owns the exclusive licence. For those who did not download Odex titles, but are served a letter of demand, Odex has no cause of action against you.
For those who did download Odex titles, Odex can bring an action against you. Whether they can prove their case against you is a question of fact and not law.
If you download titles without licence, whether such titles belong to Odex or otherwise, and the other elements making the act an offence are satisfied, a charge may be made against you by the public prosecutor.
I think deadpixel is saying that under the law, the act of downloading is an infringement against Odex's rights as exclusive licensee. No number of good lawyers can argue against the fact that under the law such act constitutes an infringement.
Also, I do not think he was trying to say that Odex has a good case against the alleged infringers (i.e., Odex possess strong evidence). For those that believe Odex would have a difficult task proving its case - by all means do not bow to their demands. Whether or not it can be proven in court, if one did indeed download the titles, it is an infringement.