No, you were right the first time, and if Erik disagreed he was uncharacteristically incorrect.
From the perspective of each amplifier channel a given output voltage will result in twice as much current being drawn from that channel in bridged mode than in stereo mode. That is because in bridged mode a voltage that is equal in magnitude but opposite in polarity will appear on the other side of the load, driven by the other channel, resulting in twice as much voltage across the load than each channel is outputting individually.
Twice as much voltage across a given load means twice as much current, of course, per Ohm’s Law (stated for this purpose as I = E/R; if E is doubled and R remains constant I is doubled). And from the perspective of each channel having to deliver twice as much current for a given output voltage corresponds to each channel "seeing" the load impedance divided by two, again per Ohm’s Law (stated for this purpose as R = E/I; if I is doubled and E remains constant R is halved).
The factor of 4 relates to power, not to impedance, as doubling the current into a given impedance corresponds to a 4x increase in power. As I’m sure you realize, for a resistive load Power = (Current squared) x Resistance.
So for an ideal design a bridged amp can deliver 4x as much power as each channel can deliver by itself, in stereo mode. In practice, though, current capability and thermal limitations usually reduce the factor of 4 significantly.
Best regards,
-- Al