Although this is a possible explanation, do you consume APIs using HTML forms? Probably not. And if you desperately have to consume APIs in the browser, you'd end up writing some JavaScript.

Sure you can, although you need to do it via Ajax.

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.

[1] http://stackoverflow.com/a/166501/1713079

I knew there was a simple explanation that I was forgetting.

you also can't PUT from an embedded flash app

Although this is a possible explanation, do you consume APIs using HTML forms? Probably not. And if you desperately have to consume APIs in the browser, you'd end up writing some JavaScript.