Tina says so in this interview from a couple of years ago for MeTV that I found on Youtube:

https://www.youtube.com/watch?v=pfZ6ZWzwgd0

She says that she had to go through three interviews, one with Fred De Cordova, one with the producer, and one with Fred MacMurray and his wife, June Haver. Fred liked her right away and he held a lot of sway so she got the part over at least 200 other actresses.

She goes on to say that Don Grady protested her being cast as Katie because he thought Katie should be played by a "super skinny surfer girl type with long hair"...??? Who knew? After she said that she chuckled and said, "And that obviously wasn't me!"

Well, I for one am glad that Tina got the role. Somehow she just "was" Katie and I can't even picture a skinny surfer girl having the grit to raise triplets and put up with Uncle Charley. Good call, Fred MacMurray! :)

I couldn't imagine anyone besides Tina Cole playing Katie!! She was beautiful and cool, really fit in with the Douglas family;)! This surprises me that Don didn't want her for Katie, , I thought Robbie and Katie had really good romantic chemistry together.:)

She had played several bit parts on the show before. I wonder if she and Grady just didn't get along for some reason. Like Vivian Vance and William Frawley.

This comment can be found in the trivia section of the IMDB M3S page:

"Don Grady almost left the show when Tina Cole was cast as Katie. In an interview, Cole revealed that Grady felt she wasn't his type. As it turned out, they eventually fell in love in real life and almost got married not once, but twice."

Interesting, especially since she was married to someone else from 1965-1970 if you can believe Wikipedia. That's a very tight timeline!

Maybe the late Mr. Grady would have preferred to have had her continue playing a beatnik with himself having stayed one.

Well, the chemistry definitely was there (even if it may not have helped Miss Cole's first union endure).

I never heard of Stanley Livingston making any objections to Ronne Troupe playing his teen bride Polly who'd just turned 18- despite Miss Troupe herself being 25 (and five years Mr. Livingston's senior) at the time!

Those are very interesting comments by Tina regarding Don Grady's assessment.

Apparently he had a preconceived notion of what Rob's California bride should look like, and Tina didn't fit the image. But she was a pretty, slender blonde lady, and if her real-life personality came close to Katie's, it's no wonder that, at a time or two, Don wanted to marry her. (We have to be a little cautious regarding IMDb trivia, because any member could add unsubstantiated stuff -- maybe it was only once that they contemplated marriage?)