Companion planting is a traditional planning method used in small gardening practices. Horticultural science studies often come up either proving, or disproving some principals of companion planting. Heres what I think about this: Traditional knowledge is built up over centuries from the experiences of living in a specific environment. One could argue that this applies to a specific lifestyle as well like subsistence agriculture or gardening. Traditional knowledge and folklore are becoming recognized as important knowledge disciplines alongside science. Companion planting passed down to you from anyone, in any form deserves it's recognition. You should choose weather or not to follow the principals of companion planting passed onto you regardless of what horticultural science says for the sake of tradition and the many years of knowledge held behind those traditions. So I say go ahead and follow traditions you were taught be it from North America, Britain, Italy, or any other cultural tradition you've been exposed to.
I've received teachings about growing the Three Sisters, corn, beans, and squash, together in many forms. But heres a helpful document that outlines this type of companion planting and also conveniently lists companions to most common garden vegetables in a table.
Helpful companion planting guide available from this page:
https://attra.ncat.org/attra-pub/summaries/summary.php?pub=72
