In many jurisdictions, a beer can be called “non-alcoholic” if it still has alcohol in it, below some threshold (usually 0.5%, some over 1%). Most people I know in recovery won’t mess with it, won’t eat food cooked with alcohol, etc. Now, even orange juice will have some naturally occurring alcohol content. Vinegar can have residual content as well–trace amounts, say a single drop in a tablespoon. But in recovery, many people’s perspective is to not tempt the fates with something where you know there is likely some alcohol in it.
To your point, though, there is non-alcohol beer that has 0.00% alcohol listed, but even for those, I’m not sure that can’t mean 0.001% in some instances. And for a non-alky “faking it,” it’s all probably fine.