Paul, One thing you may try to do is to send a letter to the editor of Journal B appealing the decision. From your description it appears that you submitted the paper to Journal B at about the same time as the other person submitted his paper to journal A so you can mention this fact and ask that your paper will be refereed on its own merits and not be rejected just based on the appearance of the other paper.

Of course, in order to be accepted your paper should be found to be correct and it is also possible that there are other distinctions between the two papers that contributed to the outcome.