Not letting them in for an inspection can also bring about trouble... It is your legal right to refuse, but it can bring more problems... A pissed off city official might not be the best idea right now...
I would check into it deeper like Lisa suggested. I've read through a few of the sections and DID find something that can be used against you:
In the original property standards by-law 1991-111:
(XXIV) "Health Hazard" means:
1. A condition of a premises,
2. A substance, thing, plant or animal other than man or,
3. A solid, liquid, gas or combination of any of them
that has or is likely to have an adverse effect on the health of any person in the opinion of the Medical Officer of Health for the region of Halton or a public Health Inspector appointed to administer the Ontario Health, Protection and Promotion act.
I haven't read through all the articles and only the beginning of the one that I quoted above.
I would strongly suggest that you temporarily move any animals that can be considered dangerous, i.e. scorps, tarantulas, very large snakes... Let them come and inspect and once they are gone you can have you animals back.
I wouldn't try to argue with them... Chances are you won't be able to convince them that all your inverts are "safe".
Anyhoo, you definitely have to research your by-laws more. I wouldn't be surprised if there was more to be found in them about your predicament...
I wouldn't chance much in your shoes. Better not have my critters for a little while than have problems with the city that could continue for longer than just this incident.
Having certain animals out publicly is never the best idea. You never know who will see you and how they will react. I know that most of the "general" population does not like knowing that their neighboor has inverts or reptiles... I would suspect that some neighboor seeing one of more of your exotic animals called the city and lodged a complaint...
Keeper of 5 snakes, leopard geckos, 1 green iguana, 20+ tarantulas, 2 dogs & a bunch of rats!