As defined in this article (% of people self-employed / owning small businesses), I think there are some other factors involved. I only know about Greece first-hand (about half my family lives there), but one reason there is that regulations and incentives generally discourage large corporations from entering a whole lot of markets, though they've been relaxed somewhat recently.
For example, Greece's high self-employment rate includes a lot of one-man grocery store or fruit/vegetable stand operations, because large supermarkets were more or less banned until recently. More generally, there were (again, recently relaxed) regulations on how many hours you could have a retail establishment open per week, and what hours they could be, intended to make it easier for small businesses to compete with the large ones: a one-man store can't reasonably be open more than maybe 60 hours/week, so the law generally banned businesses from being open more than a certain number of hours a week, and required them to close at least one or two days a week (depending on market segment). That made it much easier for small operations to compete with the large ones, because your mom-and-pop store open 6 days a week, 8 hours a day, wasn't up against a 24/7 chain store.
Some though is perhaps just cultural. When a rich Greek builds a vacation villa, for example, he'll typically get a independent architect to design it and oversee its construction, rather than going with a big design/architecture/construction corporation, which is seen as too cookie cutter / less prestigious. I bet just architects alone account for several thousand of the self-employed Greeks, whereas most American architects work for corporations (exceptions only on the very high end of world-famous architects). It even extends to commercial real-estate: the typical 6-story office or apartment building in Thessaloniki or Athens is designed and built by a small independent firm.
For example, Greece's high self-employment rate includes a lot of one-man grocery store or fruit/vegetable stand operations, because large supermarkets were more or less banned until recently. More generally, there were (again, recently relaxed) regulations on how many hours you could have a retail establishment open per week, and what hours they could be, intended to make it easier for small businesses to compete with the large ones: a one-man store can't reasonably be open more than maybe 60 hours/week, so the law generally banned businesses from being open more than a certain number of hours a week, and required them to close at least one or two days a week (depending on market segment). That made it much easier for small operations to compete with the large ones, because your mom-and-pop store open 6 days a week, 8 hours a day, wasn't up against a 24/7 chain store.
Some though is perhaps just cultural. When a rich Greek builds a vacation villa, for example, he'll typically get a independent architect to design it and oversee its construction, rather than going with a big design/architecture/construction corporation, which is seen as too cookie cutter / less prestigious. I bet just architects alone account for several thousand of the self-employed Greeks, whereas most American architects work for corporations (exceptions only on the very high end of world-famous architects). It even extends to commercial real-estate: the typical 6-story office or apartment building in Thessaloniki or Athens is designed and built by a small independent firm.