That is completely false, at least the rocks holding bad bacteria part, in fact the opposite is true rocks provide more surface area for the nitrifying bacteria to colonize. if you use rocks with rounded edges in the pond the koi won’t hurt themselves on it during spawning season. Many on here myself included have rocks in our ponds without any issues, my current pond is going on 13 years old and rarely have issues with injured fish, other than some minor injuries during spawning time.
Will add with sturgeon, know how big the species you get achieves as they can get immensely large well over 10’ long. All but the largest of ponds wouldn’t be able to handle this fish. That being said there are species of sturgeon that stay around 4’ long….still requiring a large pond but not really much different than pond sized properly for koi.