A swim through is where you can clearly see the exit before you enter, there are no entanglement hazards, the area is big and open enough for two divers swimming abreast and the exit can be easily reached at a normal pace in less than 5 seconds.
		
		
	 
This is very similar to Rick Murchison's definition of a swim-through, and I think it's a pretty good one.  
To think about this logically, we have to ask what the dangers of overhead environments ARE.  There are two.  One is that you run into a problem which would be neatly solved by ascending, and you can't, because you're trapped beneath an overhead.  Another is that you can't LEAVE the overhead, either because you are physically trapped there, or because you cannot find your way out.  
The second problem, I think, one can assess much of the time.  When I'm looking at a simple rock arch, the likelihood of getting lost in it is zero, and the likelihood of dropping the visibility enough so I can't get out from underneath it is equally small.  When you're peering into the side of the Saskatchewan, the likelihood of getting lost is significant, and the likelihood of encountering a lot of silt is also high.  In the middle are things like the 
bow of the Rhone in the BVI.  There, you could see the exit from the entrance, there were slits admitting light all along the passage, and there was no silt on the bottom.  There were no branching passages, and there was no way to get lost.  
At that point, you have to think about the first risk I mentioned.  Tear your diaphragm on the second stage halfway through the Rhone and suck water . . . Are you going to have the presence of mind to calmly being using your secondary regulator, or can you reach your buddy for gas?  Catch your fin in an interstice in the structure -- Are you going to panic and bolt?  Lots of evil things can happen to people in a "benign overhead environment", if they're inexperienced or don't know what their own personal reaction to stress underwater is.
The easy answer is to say, "Never swim into any overhead environment, until you have done formal training for doing so."  The more complex answer is to say, "Anything dark, spooky, complex, silty or manmade, or anything where you can't see the exit from the entrance, or anything where there are multiple navigational choices to be made, is too risky for someone without training.  Simple swim-throughs, where you can see the exit from the entrance, light is excellent, and silt is not an issue, must be evaluated on a case-by-case basis, erring on the side of conservativism if there is ANY doubt."