Though I wouldn’t want to overstate the case, it’s worth noting that the “acidophilus” in Lactobacter acidophilus means acid-loving. At the very least, it’s probably more acid-tolerant than most. Lactobacter refers to the fact that it is tolerant of, and even likes, lactic acid.
Various species of bacteria in geysers, hot springs, and other acid environments, thrive at pH levels like that of stomach acid - Helicobacter pylori actually lives in the stomach itself. (H. pylori, and not excess acid secretion, is responsible for most gastric ulcers. It irritates the stomach wall and breaks down the protective mucus layer. One standard test in diagnosis and treatment of ulcers is the hydrogen breath test (H pylori gives off hydrogen), if it’s positive, we may prescribe antibiotics for a cure.
BTW - not all food poisoning is caused directly by the bacteria itself. Many are pre-formed toxins. You can cook foods contaminated by such strains and kill the bacteria, but if the toxin is heat -stable, you’ll still get food-poisoning.
Other bacteria can survive stomach acid either by ‘shutting down’ or in the form of spores. Clostridia is a notorious spore former. (The most famous is botulinus, but botulism is a pre-formed toxin) Hospitals have serious problems with hand-to-mouth nosocomial spread of infections like Clostridium difficile, which set up shop in the colon.
Most importantly, the studies have actually been done on live culture yogurt. We’ve fed them to people, and observed the change in the microbial populations. We’ve even fed people labelled bacteria, so that we could confirm that they were not just the same species, but the very same bacteria that went in via their gut.
Common sense may tell you that nothing can survive a bath of strong acid, but *It just ain’t so. * Furthermore, the exposure that L acidophilus may not be all that strong. Yogurt is largely pre-digested (in terms of the physical and physiological markers your gut uses) so your stomach will start squirting it into your duodenum in little dribs almost as soon as you eat it. In the duodenum, pancreatic juices immediately neutralize the acid with bicarbonate (if this process failed, you’d get a duodenal ulcer, which is different from the gastric ulcers I mentioned above.) Yogurt is also modestly buffering, by itself.
If you have a cup of yogurt on an empty stomach, some of the bacteria will only get a small, brief, buffered-to-weakness dose of acid (which it isn’t particularly sensitive to, anyway) . In under a minute, “doses” of the bacteria are squirted to safety in the small intesting. It doesn’t take many of them to effect a change. They do multiply, after all, and you’re putting them in your gut along with a growth medium (the yogurt itself) that they favor, and which they were happily eating already. They are already in full-gear reproductive mode. The other bugs in your gut may be able to eat those same nutrients, but they’d have to change biochemical gears first.