The poster you're replying to is wrong (and he wrote what most believe). Your explanation is closer, but you're describing a RR (relative risk) not an OR (odds ratio). A 1.85 OR means drugged patients have 85% higher odds than placebo patients of ≥X improvement.
To understand how OR and RR differ, gotta understand the difference between chance and odds. Not going to get into all that, but this might be helpful for some: a horse has a chance between 0 to 100% of winning a race but its odds can be between 0 to infinity. Yes, big difference. So understanding what an OR is saying is important.
Btw some folks have been trying to reverse engineer the trial's OR's, but since they're using the wrong calculation, that's why they can't back into them.
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