shorts and the meter
The field windings are a coil which can short to ground but also can short from winding to winding. This is like taking 2 smaller power wires and connecting them together in effect making a bigger wire hence reducing resistance. Some shorted windings are okay but eventually or it could be a short to case or ground
try a good multimeter like a Fluke or try to check the accuracy of yours on some known rsistances
Normally shooting wires I would say dont worry about small differences in resistance values but in this case the diff between 0 and 4 ohms is important
So you may already have found the prob or your meter is crap
Let us know how it goes!
This guy does a good job of describing alternator short faults
Ron Kilber's Logbook - Aircraft Charging Systems
he is talking aircraft but the principal is the same
"Second, a good, sensitive ohm meter must be used to check the condition of the field winding (an inexpensive ohm meter can't accurately measure four ohms). This is done by disconnecting the regulator (with engine and master off, both sides) and placing one lead of the ohm meter to ground, the other to pin "F" of the connector, which joins the wire to the alternator's field. If it's a dead short (zero ohms), it will cause a frequent problem with malfunctioning systems: a broke voltage regulator (shorted main transistor). The system works only momentarily, then shuts down or overcharges all the time. The voltage regulator and the shorted alternator must be replaced or overhauled.
Field resistance should never be less than four ohms and must be checked by rotating the propeller to include measurement while the brushes rotate 360 degrees around the slip rings. If the resistance is too high or fluctuates too much as the shaft rotates, the brushes or slip rings could be defective. The alternator will charge very little or not at all.
With infinite resistance, on the other hand, the field winding could be open (broke) or the wire to the alternator is loose or off. The system will not charge at all. Improper field resistance usually indicates that a new or overhauled alternator is needed."