If you had a codebase that was developed over a few years by 200 different remote contractors, thats a recipe for disaster regardless of their nationality.
Why should it be any more of a disaster than an open source project?
I would wager that open source projects are most likely some of the best run projects in the world.
For one thing, an open source project typically has a stable set of one or more core contributors, who really care about the project.
An open source project is primarily composed of people writing some software out of passion with few hard deadlines. A team of 200 developers, some off shore, are developing in order to get paid for a client who likely has strict time and budget constraints. I'm not sure I could come up with many scenarios that I would expect to see a wider gap in code quality, even if the developers were the same level of skill.
Also it's easier to nope a bad decision for OSS. Office politics makes it way difficult.
I suggest that you (re)read Cathedral and the Bazaar if you really are curious about the difference between a project worked on by 200 odd developers in a company and an open source project.