Linebreeding and inbreeding is pretty common in betta breeding to achieve the cleanest lines for color and/or form (aka tail shape).
It is not uncommon for breeders to take a male and female from the same spawn (aka siblings) who most strongly resemble the trait(s) they are trying to get and then breed them back together for the next generation of bettas, hopefully more of which will demonstrate the trait they were breeding for. When they've gotten the desired trait, they then take another betta from some other line that they like, and then breed them together, and start the process with their fry all over again, or then breeding one of the spawn back to the original parent as needed for a stronger boost from that particular original 'trait' as needed.
This process is how we've acheived most of our tail types today, snce many of the more uncommon types like Double tail and Half Moon are reccessive. So careful inbreeding was required to accentuate the larger tail and shape to develop HMs, as the veiltail shape is naturally more dominant. Same applies for color. Blue is more dominant than red, but it is an incomplete dominance, which results in what you see in most pet store bettas, who are a bit red, and a bit blue.
But since none of us are worried about creating the 'perfectly colored' betta for show purposes (and thereby breeding, since that's what most show bettas are for, showing these new strains that have been developed for more breeding), we really need not worry about our bettas having multiple 'paintball' colorings on them. It's a matter of what you personally find to be pretty looking, and if you like your bettas red and purple, then by all means, have a red and purple betta!