First, this is a kit, so the fabric that comes with the kit is 15 x15. According to the description, on 18-count fabric the finished picture will be 11" x 11".
Yes, you could stitch this on 14-count fabric, but your finished picture will be 14 1/4" x 14 1/4".
A way around this would be to buy a piece of 14-count fabric that would give you more fabric for framing and take the 18-count fabric you get in the kit and save it for a smaller project. Some stitchers add 2" extra of fabric to each side to allow for mounting and framing. Personally I add 3 inches to each side to allow for mounting, possibly matting and framing.
I'm not an employee of ECS, but one of the stitchers that saw your "chat".