Is putting a div inside an anchor ever correct?

Depending on the version of HTML you're catering to:

• HTML 5 states that the <a> element "may be wrapped around entire paragraphs, lists, tables, and so forth, even entire sections, so long as there is no interactive content within (e.g. buttons or other links)".

• HTML 4.01 specifies that <a> elements may only contain inline elements. A <div> is a block element, so it may not appear inside an <a>.

  Of course you are at liberty to style an inline element such that it appears to be a block, or indeed style a block so that it is rendered inline. The use of the terms inline and block in HTML refers to the relationship of the elements to the semantic structure of the document, whereas the same terms in CSS are related more to the visual styling of the elements. If you make inline elements display in a blocky manner, that's fine.

  However you should ensure that the structure of the document still makes sense when CSS is not present, for example when accessed via an assistive technology such as a screen reader - or indeed when examined by the mighty Googlebot.

No it won't validate, but yes it generally will work in modern browsers. That being said, use a span inside your anchor, and set display: block on it as well, that will definitely work everywhere, and it will validate!

The W3C doc doesn't use concepts like wrong and sin, but it does use those like provide the means, may be appropriate and discouraged.

Actually, in the second paragraph of section 4, the 4.01 spec itemizes its words as follows

The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in [RFC2119]. However, for readability, these words do not appear in all uppercase letters in this specification.

With that in mind, I believe the definitive statement is in 7.5.3 Block-level and inline elements, where it says

Generally, inline elements may contain only data and other inline elements.

The condition "generally" appears to introduce enough ambiguity to say that HTML 4.01 does allow inline elements to contain block elements.

Certainly, CSS2 has a display property value, inline-block, that appears to be suited to the purpose you describe. I'm not sure if it was ever widely supported, but it seems that someone anticipated the need for that kind of behavior.

The DTD appear to be less forgiving here, but the text of the DTD defers to the spec:

The HTML 4.01 specification includes additional syntactic constraints that cannot be expressed within the DTDs.

In another comment, you suggest that you want to make a block active by wrapping it in an anchor. I don't believe HTML prohibits that, and CSS clearly allows it. So to answer the title question about whether it is ever correct, I say yes. By the standards, it is sometimes correct.