JSON.org License Literally Says it "shall be used for Good, not Evil"
Crockford on JSON license (2011)
I give permission for IBM [...] to use JSLint for evil.
software - Who is held accountable in case of violation of JSON license's specific 'no evil' clause - the end user, the distro, or both? - Law Stack Exchange
That “shall be used for Good, not Evil” clause is a moral category, not a legal category. From a legal perspective, it is likely meaningless and/or unenforceable. Neither Debian nor users of that software should expect any legal risk for using or distributing the software.
However, software under that license will never make it into Debian because it violates the Debian Free Software Guidelines. The DFSG is not a contract in the legal sense, but it forms part of the Debian social contract with its users. It is not in the interest of the Debian project to include software unless the software is free to use for any purpose. While the JSON license's usage restriction is likely meaningless in practice, it clearly tries do do exactly what the DFSG wants to prevent.
In the Open Source community, there is a broad consensus against the JSON license. The DFSG, slightly edited, was adopted as the Open Source Definition. Consequently, the JSON license also fails to be an Open Source license. The Free Software Foundation also looked at the license, and concluded: “This is a restriction on usage and thus conflicts with freedom 0. The restriction might be unenforcible, but we cannot presume that. Thus, the license is nonfree.”
"Say the Debian Project were to distribute jshint". That's distribution, not use. The distinction matters. This line is appended to the MIT license, which starts by enumerating different rights including both "use" and "distribute". Hence it's reasonable to assume that the term "used" in both clauses means the same. In other words, your assumption that "distribution" is the same as "use" is wrong, else the MIT license wouldn't have spelled that out.
While the MIT license allows relicensing under narrower terms, and JSON's license does not change that, removing an obligation is relicensing under broader terms. That's why IBM needed another license straight from the original author.