The multiple access channel (MAC) capacity with feedback is considered under feedback models designed to tease out which factors contribute to the MAC feedback capacity benefit. Comparing the capacity of a MAC with ``perfect'' feedback, which causally delivers to the transmitters the true channel output, to that of a MAC with ``independent'' feedback, which causally delivers to the transmitters an independent instance of that same channel output, allows separation of effects like cooperation from alternative feedback benefits such as knowledge of the channel instance. Proving that the Cover-Leung (CL) achievability bound, which is known to be loose for some channels, is achievable also under (shared or distinct) independent feedback at the transmitters shows that the CL bound does not require transmitter knowledge of the channel instance. Proving that each transmitter's maximal rate under independent feedback exceeds that under perfect feedback highlights the potential power of an independent look at the channel output.