Apparently, you have no experience with infectious diseases. Horses that look to be in perfect condition can be harboring infections. Why do you think most rated horse shows require health certificates less than 30 days old, in addition to a Coggins? Not that it stops all spread of infection but every bit of precaution helps.
If you are a rescue, you should be able to evaluate horses quickly and take advantage of homes offered as soon as possible unless the horse is in poor enough condition to require stabilization.