They are just rumors but heavily said whenever Arle for smash talks occur.
From what I can gather, it seems D4E has the right for MM's game system itself and Sega has the rights for Puyo's game system. I think the story of Arle can't use her magic to attack people is coming from here.
And on top of that, Puyo characters are not allowed to have any violence actions. "No hitting, no bashing". This was also the infamous rule known by fans but it did get confirmed by Hosoyamada himself saying that Puyopuyo fighting game was cancelled due to its violency and the higher-ups stopped him. This was 2017.
He was also saying that Puyo Quest's users are more than 50% women and widely spreaded from kids to seniors. Maybe this is a one of reason they don't want Puyo characters to fight in actual combat.
I think these stories surrounding Puyo got clearer around that time because Niitani himself was revealing a lot on TV shows. I remember seeing him explaining about Puyo's situation couple of times on TV.
When Compile asked Sega for a billion loan, Sega took only Puyo's rights as a guarantee. So they didn't buy it directly according to Niitani. Apparently Sega didn't fully own Puyo's rights until 2015. MM, on the other hand, since Sega didn't ask for it, the rights eventually passed to Aiki then to D4E.
I can't confirm these are 100% concrete but this kind of story is always popping up in Japanese smash community.
https://www.google.co.jp/amp/s/game.watch.impress.co.jp/docs/interview/1075/723/amp.index.html
https://ja.m.wikipedia.org/wiki/ぷよぷよ
https://dic.nicovideo.jp/t/a/魔導物語
https://games.yahoo.co.jp/qa/detail?qid=12199147842