It does have a precise definition (the OSD[1]), but OSI does not own the phrase in the sense of owning a (registered) trademark on it. They applied for such a trademark decades ago, but ultimately abandoned the application IIRC. That said, registered trademark or no, the OSD is by far and away the most widely accepted and used definition of what it means to be "open source". I'd argue that it is a de-facto standard, albeit not a de jure standard.
Maybe I'm biased cause the word exists in French, but I'm not sure how "libre" sounds silly.
We really have to stop letting engineers name things...
1. Someone who doesn't understand open source claims that open source means source available
2. Someone who does understand open source points to the OSI definition and points out that availability of source is nowhere near enough
3. Bickering about legal matters as if trademark law is the best way to handle terminology
4. Accusations that it's essentially tyranny for the OSI and FSF to try to establish standard definitions for open source and free software, or for the rest of us to insist upon proper use of these terms
Examples:
• https://news.ycombinator.com/item?id=25367131
• https://news.ycombinator.com/item?id=25834067
• https://news.ycombinator.com/item?id=26079067
• https://news.ycombinator.com/item?id=27267367
• https://news.ycombinator.com/item?id=25364878