Your logic here doesn't make sense to me. I don't think it's unlikely at all for a separate invert system at a supplier to carry fish diseases. Unless they practice rather strict biosecurity measures to ensure water from a fish system never comes into contact with their invert system, wet hands and non sanitized equipment will instantaneously contaminate all systems. But even beyond that, these inverts collected from the wild inevitably come in with numerous possible pathogens anyways, so the separate invert system would already be full of those contaminants. Unless you're completely drying every exterior exposed surface of whatever you add to your tank, you're absolutely adding water from the supplier to your system. Furthermore, some of the most common pathogens attach to a substrate, so not adding any contaminated water won't even be that much of a benefit.
P.S. You can now say you know of someone who quarantines chaeto (or anything else living for that matter)