In terms of the logistic regression "not one" and "doing something entirely different from one" are actually the same thing. You are either 1 or 0 - what being in one or zero means substantively is not pertinant to the method.

It is traditional, because the meaning of odds ratios less than one are not intuitively obvious, to reverse the event you are maximising when you have odds ratios less than one. That is maximize 1 rather than 0 if you were initiall maximising 0 (the software have different defaults of which is being maximised). This will cause odds ratios less than one to now be greater than one. You then interpret the odds ratio in terms of what is being maximized (which of course is the opposite of what had been maximized).

Say you were initially maximising 0 and you get a odds ratio of .75. So you change the coding to maximize 1 instead. The software will automatically generate the new odds ratio for you which will be the reciprocal of the previous finding - you don't have to do this yourself. You would then say the odds of being in 1 for a one unit change in the predictor are....(whatever the new odd ratio is, I think 1.33).

What software are you using.