Speaking as one who has many charts published and would like to receive my royalties, I think Rick's description in the previous posts is fine - in a real world. Now I don't argue that Rick's action could be considered illegal by the letter of the law. Under the law, and under the wording often found at the bottom of sheet music, you can't do anything anytime anywhere for any reason in the realm of reproducing any part of the publication. That would include writing out your transposed part so you could play it.
However, if I played the arrangement I would produce exactly the same result, but I transpose at sight so I would not have to copy the part in any way. It all happens in my head. But in my head I am actually "altering" the part, which is not allowed (copyright notices sometimes say I may not alter the part in any way).
What Rick did was to move the activity that takes place within my head into his music program. The performed result is the same. The number of copies purchased is the same.
While any of this might be tough to argue in front of a judge, especially if the judge is grumpy, I believe no publisher would go after Rick.
The copyright law is intended to protect the composer/arranger from losing royalties and to prevent the publisher from losing sales. If you made Finale copies to avoid having to buy extra, available parts, surely that would be cheating folks out of money. If you further arrange an arrangement to create a new entity, that is also a violation. But since Rick simply facilitated for his skills what I might be comfortable doing in my head, nobody lost any money on the deal. There was no treble clef Bb part available to purchase. In fact, if Rick had not thought it was OK to transpose the part this way, he presumably would not have purchased the music in the first place.
I have lost track of the number of pieces I own (or have played in the CG Band) that were not possible to perform as published. They were carelessly typeset so that a page turn came in the middle of a difficult passage, sometimes within a bunch of 16th notes. They also came with a notice at the bottom that disallowed copying of any kind. In order to perform them I copied a page of the music to facilitate the page turn. Based on the printed copyright notice, that was a violation. (If these publishers were high-profit corporations, then the best course of action would be to organize the music community enough so that buyers would return any music that came this way and demand a refund. That would force publishers to take notice and actually lay out the music so it can be played without photo copying it! But in a real world, all that would accomplish is to drive even more of these struggling businesses out of business, and we certainly don't want to do that.)
[Edit] Come to think of it, if the notice says you may not alter the part in any way, that would also not allow you to correct a wrong note in the part if you take it literally. Now THAT would make a strange court case, although I think I have heard of even stranger court cases!
I know the above is not fully in the realm of allowed/disallowed in the legal sense, and therefore does not fully satisfy the points Pam brought up. But most publishers are reasonable and apply the law in a way that protects their real interests.
Rick, feel free to call on me as a character witness if you end up in court