Can these coexist happily with potatoes?

To “lasagna” or not? HerbDoc is torn:

I recently read an article by a local garden guru who proposed growing potatoes and tomatoes in a “lasagna” type vegetable garden.  Has anyone tried this and what were the results?

I currently rely on my grandmother’s wisdom which always separated the potatoes from the other crops for two reasons.  Potatoes tend to like a lower pH (5.3 – 6.0) than tomatoes (6.0 – 6.8), and potatoes will produce lots of leaves and few quality tubers if over fertilized.  Grandma also worried about scab which tended to occur if potatoes were grown in higher soil pHs.  Of course today we can buy scab resistant potato varieties, but I wondered if gardeners who tried the dual method saw any chlorosis because iron was bound up at the higher alkalinity levels.  On the other hand would the tomatoes grown at a lower pH exhibit a lack of chlorophyll and carbohydrate production due to low magnesium, resulting in pale green plants?

If you have any experience with this method, or  some thoughts on it, we’d love to hear from you.