Well, I didn't say "always", JR. ...Just on occasion.
Koiboii: What a nice surprise you have tossed in! Lots to say, but little time. I'll assume the source spoke correctly....
First, parentage is important. That is what the varieties are all about. The more refined varieties (genetically refined)are relatively pure in their offspring. But, even Kohaku linebred for many generations beget shiromuji and benigoi. Showa is the less refined of the gosanke varieties and more likely to throw 'pondgoi'. The special qualities of the original Showa were in the overall package of powerful presence, pattern and being tri-color. However, the sumi was sooty, not deep black; the Hi was yellowish; and the body often 'stubby'. Kohaku was bred into Showa to brighten the red pigment, improving the body along the way; and Sanke was bred into Showa to improve the black pigment. The early Showa could be accurately described as black fish with white and red patterning. Long ago now, that really changed. Showa remains a black-based koi, but the ground color is white with red and black patterning as in Sanke. But, it is a different patterning derived from the Utsuri genetic origin.
Which leads to the second point: I expect the parents were the result of heavy crossing of Sanke into Showa. There are many such offspring culled each year because they do not meet the goal for being Showa. Some get through the culling and are difficult to label because they are neither Sanke nor Showa, but simply a Sanshouku... a tricolor koi. With the enhanced quality of the modern Sanke and Showa in their genetic make-up, such koi can be beautiful creatures. However, in the genetic mixing they have lost the essence of what makes a Sanke or a Showa.
Third: The koi you posted has Sanke sumi. It is what I describe as chips of black laying over one another like confetti. It is what you find in Bekko... even those domestic Arkansas Bekko that hardly deserve pond space these days. In Showa, the sumi fills the scales like watercolor...it is more fluid, harkening back to the origin of Showa as a black-based koi. The Sanke sumi has the ability to be so thick that it is truly shiny lacquer black. Showa sumi retains a muted tone, so Sanke is bred in to improve the sumi. The best specimens of Showa will retain the essential nature of Showa, but have the thick lacquer sumi that makes a koi look like a paint-by-numbers oil painting. Your koi also has a body structure that fits Sanke and the Hi is Sanke-like. The parents may have been tricolor koi labeled as Showa by someone, but they passed on the genetics of Sanke.
Fourth: Too bad the sumi on the head is not better oriented to enhance the pattern.
Gotta go!... Lots for JR to chew on, too.