Charlly also seems to be pointing out a glitch. There have been times when I invite a friend to play who shows a green dot for being available and then I get the cross platform message.
So, as she asks, why isn't it shown for all mobile players? Answer, naturally, is that there is a glitch.
I just tested this with some alt-shot buds and it appears if I start a round on PC, and then login to use my mobile to finish it, but keep the PC gameclient open, I stay "green" and the mobile image doesn't appear. As there's still a "green dot" next to my name they can try to "invite" me to play Alt-Shot, but they get the cross-platform error msg.
The mobile icon is displayed when I log out from the gameclient and log back in via mobile and start a round.
So, I wouldn't call it a glitch. It's just the method of play can't be differentiated when both platforms remain open. If anything, a glitch might be I stay "green" and don't show as "busy". I guess it's a different server you log on to play when using a mobile device.
It's hard for me to test all the scenarios as my buds who assisted are solely PC-based players.