This is a bit of a semantic leap. Putnam objected to the use of his brief to support a lawsuit against race-conscious admissions. The article describes this brief as representing Putnam's work without the "diversity isn't always bad" disclaimer. That's a far cry from using it in a simplistic argument to say diversity is bad.
The question on the table is about race-conscious admissions. If one side's position is that using race-conscious admissions is good because it improves diversity and diversity is good, period, then challenging that premise is a perfectly valid use of Putnam's research, however Putnam might personally feel about matter.
In the article, Putnam himself is quoted as saying:
In the short term, he writes, there are clearly challenges, but over the long haul, he argues that diversity has a range of benefits for a society, and that the fragmentation and distrust can be overcome.
Great! But how the hell are you ever actually going find solutions to those challenges if you aren't allowed to bring up points like this in any situation where it might actually make a difference? And what are those benefits, exactly?