Coat colour genetics are indeed much more complicated than the mere B, b, S and s , for markings colour and white showing. For instance there are thought to be four alleles for the white 'spotting ' gene, ranging from S for no white, s (little i) for Irish spotting, where the white areas don't go over the back, s (little p) for piebald, as in cavaliers and s (little w) for mainly white. These are in descending order of dominance. In other breeds, genes, affect markings like black masks (gsds) , merle (collies), intensity of colour (labs) etc, but the basic inheritance of white showing is straightforward. If they don't carry the S allele for no white, then white will show. Therefore neither Blenheim parent can carry this and pass it on.
Ani nteresting point is that our particour dogs are not actually white with black, red or tan markings , but coloured dogs with white 'leaking' through.