When you hit up a site, such as cnn.com, does the TCP/IP packet contain the MAC address of your network card?
Could cnn.com theoretically record my MAC address?
In IPv4: Nope. They will see the MAC of the device which forwarded the packet to the server, likely their border router.
In IPv6, the 64 bit "host" part of the full 128 bit address is often automatically generated from the MAC address, and hence might be visible to the server one connects to. See also How to avoid exposing my MAC address when using IPv6?