So, to the tiny meter voltage and current it exhibits < 1 Ohm but rather more resistance to the phase line?
Principally the issue is impedance versus resistance - a meter measures resistance using a DC voltage as a source (typically a 9V battery in a digital meter like a Fluke), but the mains voltage is AC, so the current is switching back and forth at 60Hz (or 50Hz in the UK). The impedance is a measure of opposition to the AC current flow. Since we only need a marginal increase in "opposition" to prevent our breaker tripping, it is not hard to see that a small increase in the impedance at 60Hz to around 4-5Ohms or greater would prevent the breaker tripping (assuming say a 30Amp breaker).
- GY