Satya Nadella’s appointment as Microsoft’s CEO was greeted with headlines such as “Why Microsoft and Everyone Else Loves Indian CEOs,” echoing Time’s 2011 lead heralding “India’s Leading Export: CEOs.” But have Indians really risen to the top of many of the world’s largest corporations? A systematic analysis of mid-2013 data on the world’s largest firms by revenue, the Fortune Global 500, shows that at that time only three non-Indian firms were led by Indian CEOs: Arcelor Mittal (Lakshmi Mittal), Deutsche Bank (Anshu Jain), and PepsiCo (Indra Nooyi). That was exactly the same as the number of non-Brazilian firms run by Brazilian CEOs, and short of the 5 non-South African firms led by South African CEOs.

Does the paucity of Indians at the top of non-Indian Fortune Global 500 corporations mean that the late C. K. Prahalad’s assertion that “Growing up in India is an extraordinary preparation for management” was wrong? Not necessarily. Indians have indeed gone out and achieved great managerial success abroad. The proportion of Silicon Valley tech startups led by Indians has risen from 7% in the 1980s and 1990s to at least 13% and by some estimates more than 25% (even though Indians make up less than 1% of the US population). One estimate pegged the annual income of the Indian diaspora at about one-third of India’s GDP, with much of that coming from Silicon Valley.

The real myth is not the success of Indians abroad but rather that the world’s largest firms are so global that their national origins no longer influence who they select for CEO. Only 13% of the Fortune Global 500 companies are led by CEOs who hail from outside the country where the firm’s headquarters is located. Also, the foreign countries where Indian CEOs do lead Fortune Global 500 firms are illustrative of how openness to foreign CEOs varies widely from country to country. European firms, on average, are the most likely to have foreign CEOs. U.S. firms lie in between European and Japanese firms.

Firms’ propensity to hire foreign CEOs is also highly correlated with their home countries’ general openness to trade, capital, information and people flows as measured on the Depth Index of Globalization that I compile with my IESE Business School colleague Steven A. Altman.

India’s fame as a CEO exporter must be juxtaposed against the paucity of non-Indians running major Indian corporates. After the untimely demise of Karl Slym, who briefly headed Tata Motors, none of India’s eight Fortune Global 500 firms is led by a non-Indian CEO. In fact, only three of the 112 Fortune Global 500 companies based in any of the BRIC countries are led by a non-native CEO! As firms from these countries seek to differentiate and build brands in advanced economies rather than competing mainly based on low home-country cost bases, the troubling signal this sends to foreign talent about their career prospects will become increasingly important.

Returning to Microsoft’s selection of an Indian CEO, it is interesting to note that one source estimates that more than one-third of Microsoft’s workforce is of Indian descent. Microsoft also earns about half of its revenue outside of the United States. The appointment of a non-native CEO of any origin is still an unusual occurrence, but Microsoft’s selection of an Indian was, all else equal, not entirely surprising. And it sends a very positive message to high-potentials throughout Microsoft: this is a company where the best candidate, regardless of national origin, can rise to the top.