The W3C FORM element is specified with only 'get' and 'post' as permissible values for 'method', which I can only regard as a screwup on W3C's part, but I know of no similar restriction on the methods available to an XMLHttpRequest object; indeed at least one extremely well-regarded Stack Overflow answer [1] confirms that PUT and DELETE work as expected as of five years ago.
POST is not - so possibly it's considered safer to use among muggles.
I also think PUT and DELETE are not cacheable, while POST is (given the right set of headers).
caveat: I might be completely wrong about my interpretation.
The real problem with trying to conform to REST is that there's no rigorous definition, and this leads to the same verb being used for slightly different purposes among APIs.