Battery Charging Issue

Your test would have been more thorough if you'd cut on the hi-beams and heater (if you had one) to subject it to a load - just like if you went into a garage to have them do it.  They introduce a load to see if your alternator is producing enough amps.  That load also helps identify a faulty regulator.  

However, since you witnessed an increase in rpms and your electrical system also increased to the correct 14volts, you identified a load that was creating a drain and removed/disconnected it.  I would suggest getting the battery tested.  They can fail in multiple ways. This internal resistance is one symptom.  My guess is that if your battery was actually okay, and your system wasn't charging as you've noted (<12V), then removing the cable from the post would have most likely caused the engine to die - as you've now removed the only adequate source of electricity (i.e. bad alternator/regulator).  Your test showed the opposite.

I agree with taking it in.  A parts store that offers this test can sell you a battery right then.