Was Buster Keaton really Charlie Chaplin's rival?

According to IMDB, Keaton and Chaplin were rivals at first, but consolidated their relationship when Keaton's career declined:

He and Buster Keaton had an interesting relationship. Long considered rivals but always having avoided commenting about each other in the press, Chaplin hired Keaton for a part in Limelight (1952). Keaton, who was flat broke at the time, went into a career decline after having been signed by MGM in 1928, as the studio would not let him improvise in any of his films nor allow him any writing or directorial input, and he was eventually reduced to writing gags - often uncredited - for other comedians' films. Chaplin, at this point, felt sorry for Keaton due to his hard luck, but Keaton recognized that, despite Charlie's better fortune and far greater wealth, Chaplin was (strangely) the more depressed of the two. In one scene in "Limelight", Chaplin's character was dying. While the camera was fading away, Keaton was muttering to Chaplin without moving his lips, "That's it, good, wait, don't move, wait, good, we're through." In his autobiography Keaton called Chaplin "the greatest silent comedian of all time".

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So while they probably never became friends, they seem to at least had professional respect for one another, which is indicated by Chaplin inviting Keaton to his movie and Keaton's acknowledgment of Chaplin's performance.

They were rivals because they were going after the same fan base. Chaplin and Keaton were both masters of "Physical Comedy", a type of comedy that relies on what can be seen as opposed to what can be said. Being they were from the "Silent Era", that makes sense, however, few were able to truly master it and those few became the biggest stars. Keaton and Chaplin were definitely the 2 most well-known from that era, and each had to push their art in order to get viewers to spend their money.

Rivals aren't always enemies. Rivals also push each other with their drive to be the best. If you've seen the movie Rush that came out last year, the ending tells (in narrative form) how the 2 drivers were rivals but not enemies.

Some of Buster's films were produced by United Artists, a company founded in part by Chaplin, so one would think that they had to have been on friendly terms, at least in a business sense.