My source was "My Great Predecessors, Part I" by Kasparov but there is no attribution. He also says that AA's first challenge to Capa was a bluff and quotes AA as saying, "I did not feel fully mature in the chess sense. In many fields, especially in technique, Capablanca was undoubtedly stronger than me at that time, and his main opponent still remained Lasker... Therefore my challenge had only one aim - to strengthen my candidature for the future."
Capablanca vs Alekhine
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6-3 is pretty convincing in my book.
Capablanca fans love to say that Alekhine "dodged" a rematch, but are strangely silent about the fact that Capablanca had made Alekhine jump through hoops to get a match in the first place. It's hardly surprising that Alekhine would later figuratively flip Capa the bird.
The champion would, at that time, not usually "waste his time" on an unworthy player. Of course Alekhine would prove his worth later but, in his own words Alekhine refused to play in a tournament (before their match) if Capablaca was appearing because "I was prepared to play only in the event of Capablanca not participating....At the moment I am a weaker player than Capablanca and if he had participated in the tournament he would have taken first prize, and to finish below Capablanca now is not at all in my interests."
In other words, Alekhine, by his own admission, was dodging Capa even before their match. I do not fault him for this. This was part of his strategy to ultimately win the title when the time was right. Fischer agrees saying, "Alekhine developed as a player much more slowly than most. In his twenties, he was an atrocious chess player and didn't mature until he was well into his thirties."
Given that, there was no reason for Capa to rush into a match. I believe Alehkine would probably have won the rematch but he wasn't taking any chances and so, yes Capa's supporters are justified in accusing AA of dodging a rematch because he agreed to do so and then never would.