What colloquial interpretation is there to this that you don't like? I would have read it as "Before trusting a watch, consider how well multiple watches agree with each other."

I had resolved the connotations to be along the lines of decisiveness, singleness of purpose and avoidance of confusing contradictory information. This kind of thing seems popular in in the kind of 'wisdom' expressed with that structure.

What colloquial interpretation is there to this that you don't like?

The standard ("colloquial") interpretation is that you should carry one watch only lest you become confused -- aka too much data leads to thinking and thinking is hard (and possibly painful).