I do eat watermelon without salt. Tomatoes only the little orange ones, when just picked out of the garden and still warm from the sun.
I love salt but for some reason on watermelon it just isn't appealing.
You must be getting ahold of some good watermelons, the ones in this area need salt. The tomatoes must be heirloom, thinner skinned and sweeter. Course anything you grow yourself are always better.