I've never heard the first and fourth movements played so fast. Both Busch and Serkin's musical lineage is from people who worked with and knew Brahms, Adolf Busch's teacher, Willy Hess, had studied with Joseph Joachim for whom Brahms wrote all three of his violin sonatas and Serkin's teacher, Richard Robert, was a friend of Brahms. Far as I can see their judgement of tempos for this piece can be taken as sound.
Serkin is my absolute favorite interpreter of the classical German-Austrian repertoire. Adolf Busch, Serkin's father in law, was an ardent anti-Nazi from the 1920s. After he'd left Germany in 1927 because he couldn't abide the rise of the Nazis, he publicly said he'd go back, "with joy on the day that Hitler, Goebbels und Göring are publicly hanged." If I could leave the United States I'd say the same about Trump, Ryan and McConnell.
Update: Mozart Rondo in A minor. K 511