After reading both the comphrehensive rules and the MTGCommander.net rules, it appears that the two contradict each other on whether or not effects that refer to cards from outside the game continue to function?
In particular, the Comprehensive Rules state that:
903.1. In the Commander variant, each deck is led by a legendary creature designated as that deck’s commander. The Commander variant was created and popularized by fans; an independent rules committee maintains additional resources at MTGCommander.net. The Commander variant uses all the normal rules for a Magic game, with the following additions.
903.11: If a player is allowed to bring a card from outside the game into a Commander game, that player can’t bring a card into the game this way if it has the same name as a card that player had in their starting deck, if it has the same name as a card that the player owns in the current game, or if any color in its color identity isn’t in the color identity of the player’s commander.
This makes it sound like so long as a card from outside the game would obey deck construction rules, it's legal to bring it in. At the same time, MTGCommander.net rule 10 is pretty explicitly against that:
10: Parts of abilities which bring other traditional card(s) you own from outside the game into the game (such as Living Wish; Spawnsire of Ulamog; Karn, the Great Creator; Wish) do not function in Commander.
Since CR 903.1 imports MTGC 10 into the game, how is the contradiction with CR 903.11 handled?
Yeah I think this it - it's to accommodate companions; technically the ability is not on a card in your actual deck/battlefield (making Rule 10 not applicable?) but an extra deck mechanic like Un-set contraptions, stickers etc. (although I do not know how "assemble a contraption" works on the one legal contraption card?).
EDIT: Also the inclusion of "traditional card(s)" probably gives companion wriggle room.
Rule 10 might also not apply since the companion mechanic is a special action. Still, it's a bit confusing because "Companion" is itself a keyword ability (702.139), so my guess is that while the companion ability allows you to take a special action to put the card into your hand, it itself doesn't put the card in your hand, so it doesn't apply. Companions are weird.