Judging from the picture you linked to, your pool looks to be made from paper and pencil crayon, this could be a problem!
I'd have to say that your installer screwed up by not putting blocks under the buttresses since that's one place you will get a lot of pressure from the top of the wall moving outwards.
All walls will move outwards eventually on an oval pool, it's the nature of the beast when you buy one, on a round pool they won't because pressure is equal in every direction.
I would not try to ratchet the pool back together, you can cause damage through an upright buckling, that will take your wall with it an collapse your pool, do what they suggested and drain half the pool to alleviate a lot of extra weight when doing it - this is likely their plan as well, once it's pulled in they or you will place patio blocks under the uprights - it should last at least one season, once winter frost has it's way with the pool, it'll lean outward again - maybe not as much to start but it WILL lean out.