The (apocryphal) quote is generally attributed to a Decca Records A&R executive named Dick Rowe who supposedly said it to Brian Epstein (the Beatles' manager) in 1962 who quoted it in his autobiography in 1964 and the quote then became "canon" with Hunter Davies (the band's authorized biographer) when he published it in his book (and in a Life magazine article) in 1968.
Mark Lewisohn, the leading Beatles' historian is not so sure about its authenticity.
So on to the question of what that A&R man could have meant by "guitar groups" being "on the way out". I believe one can only speculate here. Could it be that Decca was scouting the market for more solo acts instead of "beat groups"? If so, why then did Decca sign a beat group instead of the Beatles?
Brian Epstein was a brilliant marketer and he knew the power of well-crafted publicity. Could the quote simply have been a fabrication?
Could you please share your source? Decca did indeed reject The Beatles (along with all but one other label - Polydor) but they took the time to send representatives from London to Liverpool to see them live, after an underwhelming audition. (The representatives didn't make it into the Cavern, not wanting to wait in the rain to get in.)
I got that from "The Beatles," by Bob Spitz.