Yes, stumbling is the universal answer when there is no scripture or worse it is supposed to be a "conscience matter." Even if it is only one person, rest of the congregation must dance to their tune; and of course, the elders will never name the person that might be stumbled or what that person's reasoning might be.
My experience, most often it was that particular elder's wife who did not like something I was doing. I would just point out the elders and/or their wives who were doing the same thing. Then it was dropped.
Of course, if you were the person who was "stumbled," you were told to overlook it and wait on their god to correct it.