On the covers, it's a gray costume, but on the interior pages, it IS purple Batman is wearing. I remember asking my Mom about it, and she didn't know why they did it that way. Around 1969 or so, is when they changed the color away from purple to gray when they turned Batman into THE Batman.
It's funny because the first color episode is saw was in a sears store and the leotard appeared lavender. Also, the German comics make the costume out to be lavender or even darker.
Now we know better.
I recall a similar discussion regarding the comics, was the cape blue or black in the original detective issues.
Thank goodness Bob Kane didn't get his way or we'd have the Bat Scarlet Pimpernel...