Simple answer to the final part is "No". Misty is one tune that doesn't lend itself well to being played in thirds.
I think the quote is addressing tunes that are scalar, where there are runs up and down, consecutive note wise. Misty doesn't do that, and there's the added problem that thirds assumes playing a diatonic note a third (be it maj or min) above the melody note. Try it with Misty, and the new notes don't match the chord for that part.
Which is probably the crux of the matter. The harmony in thirds must work with the chord, otherwise it will sound bad. Let's try something more scalar - Fly Me to the Moon. First bar Am(7). Tune - C B A G, harmony E D C B all fits - the G+B is on the weak part of the bar. Next Dm(7). Tune F G A C, harmony A B C E - again, the C+E on the weak part. So it continues in thirds and fits well.
A problem may occur when, say, the chord , in C, is C, but the main melody note is G. Put a third above this - B - and it often won't match the chord. Obviously if it's Cmaj7, it will; but not over a plain C chord.
When a tune jumps about, it's not easy, or suitable, to harmonise in thirds - the upper note doesn't always work. As a technical exercise, it's an idea, as your quote, but musically can end up as a disaster.