No, it doesn't. It says that many are in favor of colleges regulating some on-campus speech that is deliberately offensive. Even to the extent that the colleges are public and thus even relevant to “free speech” considerations, that's a combination of context and intent to offend, not mere capacity to offend, that is at issue.
(It separately says that many would support the government regulating “certain types of offensive speech”, which does not provide enough information to support that the basis is mere capacity to offend; the types of things that constitute per se defamation are arguably a “certain type of offensive speech”, for instance; vague categories are good for getting big scary numbers, but weak for supporting concrete conclusions.)
I agree that it feels inflated compared to potentially less emotionally provocative question about freedom of speech as a fundamental concept.
Then again, I wouldn't be shocked if that is the the general stance of a lot of people. Speaking as a Canadian, these types of government restrictions on hateful speech are written into law and largely uncontested in politics.
http://www.pewresearch.org/fact-tank/2015/11/20/40-of-millen...
I really don’t understand people who are more afraid of a racial slur (to be clear, I strongly disapprove of that kind of thing) than of losing freedom of thought and of expression.
Prohibitions where intent is an essential component, and judging intent is essential to applying the prohibition are not new in campus regulation, or in civil and criminal law, for that matter.
But, in any case, that's in implementation issue that is not germane to what support has actually been voiced for.