Using stock seamless pattern files to make pattern swatches.

I have some seamless pattern EPS files which I downloaded from iStock, to use in Adobe Illustrator, to make some pattern swatches, to fill some rectangles. With some of the files, I can just select the pattern square and drag it to the swatches (or the pattern is already in the swatches panel when I open the file) and so I can then easily fill rectangles with the pattern.

But, with some, this does not work. When I select the pattern square and drag it to the swatches panel, it creates a swatch, but with a white border around it, and then when I fill a rectangle using this pattern swatch it appears as lots of separate pattern squares surrounded by grey.

Does anyone know how to resolve this problem? Thanks in advance!