I would wait until the bed is in the space before choosing paint , your light will have an effect on the color and gray can be a tricky color at the best of times so wait.

Yes it is very possible the gray may look green because all grays have an undertone, either green, blue, violet or blue green. In some fabrics it pops out more than in others, but it is always there. Is it possible for you to find the bed in person somewhere before ordering or get a sample of the fabric from the manufacturer? I get the feeling you aren't totally sold if its a green gray. If you go ahead with the bed then use gray paint with green undertones, for example BM Revere pewter, thunder or Edgecomb gray. You can still have white/off white trim trim with those warmer grays in order to achieve the fresh look that goes with the gray trend you are wanting.
In the photo on the computer the green isn't jumping out at me, but if people who have the bed are saying it, it must be there. This is the problem with choosing upholstery from a computer monitor, the colours are never true in my experience.

I have this EXACT bed; Kingsize. I bought it two months ago in anticipation of my move and put it in storage. Over the past 2 months I painted and re-carpeted my new home and bought a few bedroom accouterments.... THEN i brought home my bed; immediately my family/friends ask "Where's the olive green bed!"
So I know exactly what you're saying ! I posted my dilemma here under
"King-size upholstered PEWTER Bed - Help! ".....
I've a lot of feedback and ideas SO see my post & replies . I hope you find it helpful as well. BTW. I still see my bed as Olive Green... The rest of the world says Pewter; either way works- I love it!