Often it doesn't work if you play a minor scale over a major song. What they probably mean is the blues. In a standard blues you have dominant seventh chords, and they contain a major third (and a minor seventh). The appropriate chord scale over these chords is the mixolydian scale, which is simply a major scale with a lowered seventh scale degree. However, since it's a blues you can also use the blues scale, which is just a minor pentatonic scale with an added #4/b5. So in the blues you can usually mix major and minor sounds, and this is what makes the bluesy sound.
As an example, take a C7 chord:
C - E - G - Bb
The corresponding mixolydian scale is
C - D - E - F - G - A - Bb
and the blues scale is
C - Eb - F - F# - G - Bb
As you can see, the blues scale adds the note Eb, which is a minor third up from the root C, even though the chord actually contains the major third. In this sense, you mix minor and major. However, this only works if a bluesy sound is desired and appropriate, it won't work so well over "Twinkle Twinkle Little Star" ...