Not very likely. Alaska Airlines isn't in an alliance with either AA or UA. This was an isolated incident; Alaska isn't going to help you with a problem on UA or AA.
The post from MillauFr had a "smiley" after it. I think the point was to share an unusual news story, not to make a statement about any policy of Alaska Airlines.
Actually, Alaska Airlines has interline agreements with American, United, Delta, and various international airlines. Connecting flights involving Alaska Airlines and an interline partner can be on a single ticket, and baggage can be checked through from the origin to the destination (without the the passenger having to claim and recheck the bags at the connecting airport).
Beyond that, to deal with flight cancellations and other flight issues, Alaska can sign over its tickets to other airlines and other airlines can sign tickets over to Alaska. This is also true among the big legacy airlines. For example, I've had American gate agents at Chicago-O'Hare sign my tickets over to Continental and United when American cancelled my flights.
I agree that "Alaska isn't going to help you with a problem on UA or AA" under normal circumstances.
But, for example, if American or United cancels a flight out of Seattle to a destination that's also served by Alaska, passengers could be accommodated on Alaska Airlines if American or United initiates it. Generally, airlines don't like to sign over tickets to a competitor, but they do it because it's a part of the traditional way taking care of passengers.
Beyond that, Alaska is a codeshare partner with American, Delta, and bunch of international carriers. For example that same flight (on an Alaska Airlines aircraft) from Seattle to Chicago could have an Alaska Airlines flight number, an American Airlines flight number, and even a Korean Airlines flight number.
Finally, Alaska Airlines extends elite frequent flyer benefits to elite members in Delta's and American's frequent flyer programs, even if they're ticketed on an Alaska Airlines-operated flight on an Alaska Airlines ticket, with no codeshare involved.
Southwest is a notable exception to interlining with other airlines. The things I've described above do not apply to Southwest. Fortunately for Southwest passengers, Southwest's own extensive route structure and and flight frequencies usually allow it to get passengers to their destinations reasonably well, even when weather or mechanical issues affect the original itinerary.
