It's absolutely amazing just how pervasive the misunderstanding of the 3:1 rule its. Here's how it is supposed to read:
Any given microphone should be at least three times farther from the next closest miked source as it is from its own source.
All the 3:1 rule is meant to be is a guideline for reducing the amount or level of significant bleed into a microphone from an adjoining source that has it's own microphone, with the intention of keeping possible phase delay issues caused by such bleed to a minimum. Note that the 3 represents the distance to the next mic's source, not to the next mic.
If you really want to simplify the 3:1 rule, it can be stated this way:
Position your mikes to keep the bleed from the neighboring sources to an insignificant minimum so that the bleed does not cause phase issues when everything is mixed together.
That's it. That's it's full meaning. the 3:1 distance is just a general guideline (and a very good one, BTW) for minimum recommended distance based upon some very basic math rules, but is by no means meant to be a magic ratio that must specifically be adhered to. There is no magic to the 3:1 ratio itself. It could be 3.3:1 or it could 4:1 or it could be 100:1, or just about anything in-between. It can, in fact even be less than 3:1 if the bleed from the adjoining miked source is not actually creating significant phase interference with the signal in the adjoining mic.
With this understanding you'll see that the rule does not apply whatsoever to two mics miking the same source; i.e. that it has nothing to do with close mic vs. room mic.
G.