Is there a CommonJS/require() implementation that doesn't use `module.exports`?

Question

Are there any build tools or JS-environments that use only the exports-variable and not module.exports, when doing a CommonJS-like require()? (i.e. disregard AMD/RequireJS)

Background
The CommonJS specification only defines the exports variable – it never mentions module.exports – however when most people write about CommonJS¹, they assume that it's possible to use module.exports rather than exports, as popularized by Node.js. My general impression is that most so-called "CommonJS" implementations support module.exports.

This is relevant to me as the UMD-template for jQuery-plugins only checks module.exports, whereas most of the other CommonJS UMD-templates actually check the exports-variable (and thus conform to the CommonJS-spec). So which one is it – can I move to fully ignoring exports and only check for module.exports – or do I really need to check exports to have my library support all possible clients?

References
¹ dontkry.com, freecodecamp.com, Brian Leroux, various StackOverflow questions