Your parent is not talking about organic methods, but rather different varieties of crops. E.g., big red beefsteak tomatoes are popular and travel well while little heirloom varieties do not, so you are going to have access to additional, possibly more nutrative, varieties if you buy local.
This has nothing to do with "organic" anything - the conditions of breeding - but modern breeds of vegetables and fruit. There's no shortage of evidence of the difference, and the decline in vitamin content over the last many decades, in the U.S.
If you're buying a better product for a price you're considering fair, you're not meaningfully "buying local" - the product you prefer just happens to be locally produced (and possibly can only be locally produced).
The kind of buying local that you need campaigns to encourage people to do, is generally either more expensive or poorer quality than the non-local alternative.
Better is the whole point of buying local - the can't buy traditional varieties remotely because they don't ship well. Of course you COULD buy shabby shipping varieties locally, but that was never what Alice was about, and it would be a silly thing to do.
