What counts as "anaerobic" re: botulism?

Anaerobic simply means "absence of air."

Any liquid food environment basically counts as "anaerobic." Yes, there may be some dissolved gases and exchange of air may happen near the surface of a liquid like water, but deeper in an undisturbed liquid, there's often not enough air to prevent botulism growth. Some basically "solid" foods count too, if they aren't porous or are highly viscous (but apparent solids) and contain a high enough moisture content for bacteria to grow and spread. Any solids that are relatively moist and close-packed are also a particular problem (think sausages).

Whether all of these anaerobic environments will grow botulism then depends on various other factors. Botulism bacteria need food. They dislike acidity or excess salt (think pickles) or excess sugar (think preserves) or alcohol (think fermentation), which are all traditional preservation methods. They need a certain level of water -- hence why drying was also a traditional preservation method and why solid hunks of stuff are less likely to cause problems (unless they have sufficient internal moisture). Also, oil-rich environments lack water and may not grow botulism (think mayonnaise) but water-containing food within oil can (think garlic or herbs in oil).

All of these may be "anaerobic" environments, but the other factors can prevent botulism.

Lastly, you have things like temperature -- chilling will slow botulism growth to a crawl and at low temperatures stop it completely. That's the last traditional preservation method: chilling or freezing.

Basically, anything under liquid left at room temperature for extended periods could conceivably grow botulism bacteria, assuming adequate "food" (for the bacteria) is present and none of the "preserving" environmental conditions mentioned above. Note the "extended periods" -- compared to other food poisoning bacteria, botulism grows more slowly and generally needs at least a couple days to grow to appreciable levels. And that's why any type of canning recipes, etc. from official organizations are rigorously tested with exact measurements for preservation agents (like acid, salt, etc.), unless they undergo a "pressure canning" step that heats the food hot enough to actually kill botulism spores (which will survive boiling). Similarly, preserved meats (especially processed ground ones) that can remain at room temperature need to be treated with excessive salt for long periods (sometimes acid as well), and often other agents (like nitrates or nitrites) to inhibit botulism growth.

So yes, as Harold McGee mentions, stock left at room temperature for a few days can definitely grow botulism bacteria. A casserole left at room temperature for a few days could likely grow them too. Meat left at room temperature can definitely grow botulism, which is actually one of the biggest problems for actual cases of botulism after canning -- improperly preserved meat not kept under refrigeration.

"Solid" meat and vegetables are less likely to have botulism bacteria far in their interior in the first place (and often aren't "wet" enough for the bacteria to spread far), but if they become contaminated, they can be a problem too. For example: baked potatoes stored in foil and kept at room temperature have been known to be a cause, as have pickled eggs that were pricked before pickling (thus inadvertently introducing botulism bacteria into the otherwise sterile yolk).

To quote the FDA:

Botulinal toxin has been demonstrated in a considerable variety of foods, such as canned corn, peppers, green beans, soups, beets, asparagus, mushrooms, ripe olives, spinach, tuna fish, chicken and chicken livers and liver pate, and luncheon meats, ham, sausage, stuffed eggplant, lobster, and smoked and salted fish.