Jeremy,
You state you have cleaned plenty of those suites !!!
stained wooden frames , a disaster waiting to happen if you do not take precautions.
it seems to be the frames have been wet and transfered, and /or the solution has spread from material to the frame , causing the stain to transfer.
In answer to your questions. I doubt very much can be done now if its wood staining, even on carpets this can be a no no, especialy on a more delicate fabric. having said that if you are going to end up owning it you can at least try 1 or 2 things, nothing to lose .
My first suggestion would be , heat transfer redrx, then sodium meta, if this fails a bleaching agent, you never know you may be lucky

in answer to you other question.
Yes ! quite definatly you could have prevented this.
protect all the exposed wooded areas from pre spray and rinse, do not wet the areas of any material touching the wood and that cannot be removed, and finaly ensure rapid and complete drying .
Good luck
geoff