I heard that brushing teeth with white grease (inedible pig lard) reduces cavities. Is this true?
Oil pulling is an ancient Ayurvedic practice that essentially involves swishing around oil in the mouth. Similar to a mouthwash, the oil “pulls” bacteria and toxins out of the mouth and, over time, can leave your teeth whiter and your gums healthier. And while oil pulling may seem a little “woo woo” at first, many studies have proven that the practice can be extremely beneficial to oral health and hygiene.]1
I wouldn't use "never" as it's an absolute that usually doesn't work, yet there are some indications that oils may have certain oral health benefits such as alleviating halitosis (bad breath), and reducing gingivitis (inflammation of the gums).
White grease is basically inedible pig fat used as lubricant in mechanics. The studies mentioned test traditional Indian folk remedies that rely on sesame or sunflower oil, but there doesn't seem to be much indication if any about white grease.
Decreasing the amount of bacteria in the mouth could contribute to less cavities, though there's no certainty of either effect in white grease.
According to this safety data sheet on White Lithium Grease,
"INGESTION: Ingestion may cause slight stomach irritation and discomfort."
If you're willing to bear the risks of accidental ingestion (which shouldn't happen anyways if you're using it like mouthwash), then maybe you could find out for yourself.