The word botulism refers to a disease caused by the botulinum toxin, not to infection by the bacteria itself. In babies infection that then produces the toxin is the bigger risk, but in adults the larger risk is poisoning from food that has been contaminated with botulinum and that has not been stored in such a way to stop the bacteria spores germinating. So you would not have had a gut infection as I've described, you would probably have eaten the cheese and your gut would have killed off the bacteria but absorbed the toxin.

I am interested that it's cheese though! Botulism is usually associated with canned/preserved goods, and it's an anaerobic bacteria, so I wouldn't expect it to like cheese. When you say 'separated,' do you mean curdled/separated into curds and whey? I found this article that shows that dairy with botulinum contamination does curdle (as curdling is a chemical process and not an organic one, many milk contaminants do not cause it): https://pubmed.ncbi.nlm.nih.gov/10456739/

Botulinum spores can withstand fairly high temperatures and is an anaerobic bacteria; that makes it hardy against for the two major features of cans that keep the food safe. One of the real dangers of botulinum is that food safety rules that protect against other bacteria are insufficient.

A can doesn't need to be burst or leaking to get the bacteria inside because the spores are probably already there. It's when the can or jar was heat-treated at a temperature which was too low (still hot enough to kill off everything else!) or the conditions inside are not acidic enough that it will germinate from the spores and start producing botulinum toxin.

And, because it's the toxin that causes the disease, not the bacteria, re-cooking the food to temperatures that we would usually consider safe might kill the bacteria but the toxin is still there.

Botulinum is a sporing bacteria, like anthrax; in conditions it can't reproduce well in, it forms spores, basically dormant versions of the bacteria inside a protective shell that can then withstand environmental conditions, including honey.

Honey is mildly antibacterial because it has such a strong concentration of sugar that it forces all the water out of bacteria by osmosis. Botulinum in a spore can survive that and then germinate into the active bacteria if it later enters safe conditions.

The other reason honey is specifically a risk is bioaccumulation. Botulinum spores naturally occur at low levels in most soil, which means there are tiny tiny traces on most things, including the surfaces of flower—not enough to do anything most of the time. But honey is made with of a lot of pollen. It can potentially build up in the honey the same way that eg. mercury builds up in tuna; tiny fishes absorb a little environmental mercury, but tuna eat a lot of tiny fishes in their lifetime, and they can't eliminate the mercury, so they consume far more mercury than a fish the same size would absorb from the water.

Your professor is wrong; it is nothing to do with expelling the spores.

The botulinum bacteria is a poor competitor. In an environment where there are already lots of other established bacteria, it struggles to form toxin-producing colonies; babies have less developed gut flora, not just because they haven't picked them up from the environment but also because their diet is much more limited.

Adults do occasionally get intestinal botulism. This usually happens in cases where they have been on antibiotics for some time and the gut flora has been killed off.

I really recommend the This Podcast Will Kill You episode on botulism!