I have two arguments: first, it's not true that the OSI coined the term. But more importantly, it isn't even important if it was true. What matters is the context in which the open source movement emerged, and how people who use the term think of it.

The open source / free software movement was born in universities who primarily wanted to erase the barriers on collaboration between them, and wanted to follow an open model. They grew frustrated of the proprietary and opaque model of software written by major corporations. They could not use it. So they decided to write their own free software and combine their efforts to not rely on corporate or proprietary software.

Back then, corporations were uninterested in open source. In fact they were hostile to it and wanted it to die. The issue that we deal with today of corporations leeching on open source did not exist, so the fact that the movement did not specifically fight this does not mean they're okay with it. The corporate hostility took a different form and that's what they combatted.

On OSI coining the term, the OSI themselves claim it was coined by Christine Peterson. They do not claim that they founded the term, nor that the founder had an affiliation with them: https://opensource.org/history