Do PoE network switches have low output impedance and high input impedance?
Ethernet is transformer coupled.  This has the effect of separating the low frequency part (DC voltage bias) from the high frequency part (data).  In general, the high frequency part must be impedance matched to minimize reflections.  At low frequencies, you don't want current to flow down the line due to grounding differences, so the impedance to ground at DC (and low frequencies) would be high.  This also applies to PoE - you should see an open circuit to ground.  However, PoE places an isolated path between two of the signal pairs that would be low impedance on whatever end is supplying the power.  The load would then draw whatever current it needs using an isolated DC to DC converter.