So you're accusing Jordan of trying too hard to take credit? I can think of someone who has tried pretty damn hard to take credit but it isn't Jordan or John.
Why else would JR say what he said?
While Mike may have played a big role in the arrangements of the songs, so did Jordan and John. To call Mike the main arranger is like saying all Jordan and John can do is come up with random riffs and they need someone to piece them together. That is simply not true.
And I didn't say that.
They all arranged the music, including Mike. Mike had a strong voice in the creative process but most people think of a song writer as someone that is coming up with the actual music which Mike rarely did other than vocal melodies for is share of songs. This isn't to say he shouldn't receive songwriting credit. Vocal melodies are a very important part of the songwriting process.
You could get super granular with the kinds of credits people deserve and don't deserve. Should MP be a credited arranger? Producer? Writer? Additional material? It's hard to say since no one was there. But we can reasonably believe he was very involved with and very controlling of the process of jamming on the music and giving input to where it should go. Even if he wasn't creating the melodies himself, he wasn't just watching them write music and then giving his opinion. He was playing drums and giving input with the rest of the band while figuring out the songs. I don't know how that isn't writing music, unless you define the term super specifically.
But if arrangement was so important, should Kevin Shirley not take songwriting credits on Falling Into Infinity? His fingerprints were all over that one.
As far as we know, Shirley wasn't involved with the songwriting process. But he is the producer on the album for a reason.
I'm not very knowledgable about how all this stuff works, but I always thought there was a big difference between editing and writing. Editing is something that a producer - which MP was - would do, whereas actually coming up with melodies and riffs is something that deserves a writing credit. Maybe someone familiar with the legalese of it all can clarify, but I think that what Jordan said was fair.
Your post gets at more the underlying question of "what is writing?" A lot of the answer is simply legal. But in this case, it's more of a philosophical question.
The reason I mentioned editing is that people think taking pre-existing elements and deciding how they go together is mostly technical. But choosing takes and how they are edited can radically alter what the finished product is. Somewhere on the Internet, you can find a rough edit of the Star Wars Catina scene. I'm not sure if any of the takes are even different, but the timing of the cuts is completely different, and the result is nothing like Star Wars.
So, to transfer that over to music, making decisions like "this intro should be two measures vs four measures" can have a massive impact on the final product. Or saying "we should go from this heavy riff to something softer" instead of an epic section fundamentally alters what the song is. We know MP made these decisions because we have video of him doing it. And I can't think of any song written during the JR era where JP and JR sat down and wrote a song together than showed MP the result. Virtually all of it was jammed out as a group. So, if by any definition of songwriting other than "writing the melodies" MP co-wrote the music, then why would JR call it misleading to have him as a credited writer?