Not true. Miso is fermented and soy sauce is fermented. Nato is fermented with a totally different bacteria from miso and soy sauce. Edamame is young soybeans that are not fermented. Tofu is made from unfermented mature soy beans. And there are plenty of other soy based foods that are not fermented (I am not sure how common this is now, but unfermented boiled soy beans used to be a pretty large part of the typical Japanese diet). While miso and soy sauce are probably the most frequently consumed forms of soy, there are plenty of other non-fermented forms of soy that are routinely eaten (far more than in the U.S.).
I also am not certain how that affects the estrogen-like compounds, however, I do know that they are not the parts of the soy that are changed during fermentation. This means it is unlikely that there is any difference, however it is possible that fermentation by-products could react with and modify them. Again though, this is unlikely, especially given that the rather more extreme processes used in the creation of common soy products found in the U.S. have no impact (and these U.S. products are the ones that scientists did a significant amount of their research on).
The main oils found in the Mediterranean diet are from nuts and seeds. Fish oils are certainly a larger part of their diet than the average American diet, but also keep in mind that they don't tend to eat anywhere near as much meat products (including fish) as we do in the U.S. The main fact, however, is that many people in the Mediterranean region consume 40% or more of their caloric intake in oils, and a vast majority of that comes from nuts and seeds, while most of the rest comes from fish. Supposedly some people living in that region consume as much as 60% of their calories from oils, without any noticeable side effects.
I do want to be clear that this is not the only dietary difference from people in the U.S. A larger percentage of carbs in the Mediterranean diet come from whole fruits than in the U.S., where most carbs come from refined grains and starchy vegetables (specifically, potatoes).
My point, however, has nothing to do with that. My point is that high fat diets are not inherently bad. It is more complicated than that. The studies I found when I was researching this were clear that a high fat diet also required more high glycemic index carbs to cause problems. Common high fat diets in regions where people tend to have few of the common health problems found in the U.S. also include far less refined grains and other high glycemic index carbs than the typical U.S. diet that mixes both. The problematic diets are the ones that include a lot of fat along with starchy vegetables (mostly potatoes) and high sugar intake (mostly soda or fruit juices). (High glycemic index diets are also pretty unhealthy even without the fat, but together, they are significantly worse.)