Data Origin Authentication vs Non Repudiation?

I'm looking into how authenticated encryption primitives work and was wondering if non-repudiation is provided with these. Investigating further into them led to the answer being that data origin authentication (DAO) are provided by the primitives.

Now DAO is defined as "the source of the information being verified", providing integrity through MAC. Yet Non-repudiation is almost defined as the same thing, in which it provides proof of the origin and the creator of said data being unable to deny that they created the data.

If they both say the same thing, then why is it that some sources state that authenticated primitives do not in fact have non-repudiation when they do? Some say that the separate primitives that are combined result in non-repudiation being created, but I am so genuinely confused at what I'm supposed to take from this.

For message authentication the sender can repute the creation of the authentication tag as the receiver has the same key. Signatures can also be verified by other parties as they may obtain a trusted public key to do so.

Imagine the sale of a house where the seller can also create the signature under the sales contract for the buyer. That is possible under message authentication but not under a signature scheme.

Diving into message authentication

Message authentication is a better term than Data Origin Authentication in my opinion. In case of data origin authentication you'd assume that the origin might be established by a third party, is not correct for MAC or AEAD schemes.

Message authentication means that the receiving party can identify that the other party that holds the secret key has generated the message. Of course, this assumes that the party doesn't accept messages that they've signed themselves.

Protection against this kind of replay attack can be accomplished in two ways:

1. only using the secret key in one direction, i.e. for sending or for receiving;
2. having some kind of identifier within the messages that are encrypted & authenticated.

Symmetric message authentication does not work for any other parties as they don't possess the symmetric key to verify the messages.

Note that the message authentication principle only works in a two-party system. You can have an $N$-party system where $N \gt 2$, but in that case it is impossible to detect any fraudulently signed messages by any of the party members. In other words, it would require full trust of the members within the network.