The DMCA doesn't say "use your judgement to decide whether you think a takedown request is valid or not". It says "you must prosecute all syntactically valid takedown requests, and if someone sends invalid ones they can be sued".
Most specifically, GitHub has no legal standing to challenge a takedown request. The uploader of the targeted content is the only one who can challenge.
There are basically zero places online hosting content from 3rd party entities which do not honor DMCA takedowns. Given the size of copyright violation penalties, ignoring them is tantamount to corporate suicide.
"There are basically zero places online hosting content from 3rd party entities which do not honor DMCA takedowns."
This is false. I was personally involved in one very large one (190k+ source code projects) where we pushed back on clearly invalid legally (but not syntactically) DMCA requests all the time, such as for trademark violations, or claims for source they didn't own, or ...
I think you missed the point of Google Code. Google Code was not intended to "win". Google Code was intended to provide an alternative the worsening monoculture of Sourceforge, because it was becoming actively harmful to open source. In that, it succeeded wildly.
Github does not appear to be a worsening monoculture (though it is, in a lot of ways, a monoculture).
Most specifically, GitHub has no legal standing to challenge a takedown request. The uploader of the targeted content is the only one who can challenge.
There are basically zero places online hosting content from 3rd party entities which do not honor DMCA takedowns. Given the size of copyright violation penalties, ignoring them is tantamount to corporate suicide.