It's more complicated, in the 1950s did Elvis Presley or Pat Boone cover black singers version of the same songs? My answer would be yes. But, female singers like Kitty Kallen, Joni James and others in the 1950s sometimes released the same songs. ("Little Things Mean A Lot" is just one example of many.) The arrangements might have been slightly different, but the singers often sounded alike. I have no answer to this situation.
Although I tend to believe you are correct about Martin and Mitchell.