Applying pressure to foam compresses it. Feet apply pressure at varying levels and in varying places throughout each step. Midsole foam will therefore compress in different amounts, leading to different amounts of drop. The idea of "zero drop" as a flat, runner-neutral platform is therefore only other than complete and utter rubbish* when there is no midsole foam to compress, which is the case with minimalist shoes. But some people still conflate the ideas of zero drop and minimalism, with Runner's World, for example, saying "Altra's running shoes are for minimalist fiends" when some of Altra's thinnest shoes have, I believe, a 14mm midsole. (I can't verify that now because their website banned me; I don't even have permission to read their 403 error {"forbidden"} page.) If "minimal" means "of a minimum amount" (New Oxford American), and if adding foam between outsole and insole exceeds the minimum amount necessary (and none is required, see, e.g., actual minimalist shoes), then any shoe with a midsole fails to qualify as "minimalist."
Zero drop isn't even less-maximalist than traditional wedge-pillow-shoes. If you have the same amount of padding under the heel as under the toes, you'll be standing on a reverse wedge (higher under the toes) during heel-strike -- which encourages ankle dorsiflexion upon landing which, as far as I can tell, exacerbates whiplash along the anterior chain (shin splints, runner's knee, and strains leading up to the iliac crest) and its immediate counterbalance, the lower back. Also, no runner needs as much cushioning under their toes as under their heels, so that padding acts as both anchor (extra weight) and sail (to catch on things, the least of which is wind). Zero drop shoes therefore have more pillow-related problems than traditional Nike wedges.
So, I think zero-drop is a horrible idea, and I cannot imagine that anyone in good faith could call a big thick foam sheet "minimalist." I can forgive consumers for confusing the many ideas that swarm around in a big cloud called "minimalist/barefoot running", but I find it difficult to be patient with those who dance the line Tristan mentioned between making health claims that might be true but which are unsupported (like Vibram did) and making nonsense claims (which have no legal significance; they're "mere puffery") which I've seen demonstrated (in my own knees) as being substantially detrimental. Calling big puffy shoes "minimalist" to attract potential runners who understand that minimalist running might help them run without injury just smacks of malicious greed.
*If I were a gymnast, I'd be in love with zero-drop, heavily padded shoes because they more closely resemble moving across a big flat pad than anything else. In that case, zero-drop is a wonderful feature. For runners, not so much.
As a postscript: I wish running shoe companies could see barefoot running as something to embrace, not to compete against. I love unshod running, and not just because it enabled me to run in the first place. But the more I run the more I gain appreciation for different types of shoes. Traction on wet, muddy, rocky trails? I could see that being useful. Protection for when I can't see the ground? Please, yes. Warmth for when I need to stop running for a while? Great! And, recognizing that those are specialized tools, I'm willing to pay more for exactly the right product. So, if running shoe companies supported barefoot running (and otherwise encouraged people to learn to run, not just to buy shoes and get out there), there's be more runners to buy more shoes, and each might own more shoes than before. Right? I suspect the potential downside of losing a few sales due to folks not replacing their shoes every 300 miles would be more than made up for by runners who, for the first time ever, would be running more than 300 miles per year. If you disagree, that's fine. Just, please, stop co-opting our barefoot terminology to trick novice runners into buying your products.
