According to the W3 specs, <link> tags are only supposed to go in the <head> section:
References
For HTML 4.01: http://www.w3.org/TR/html401/struct/links.html#edef-LINK
For HTML5: http://www.w3.org/TR/html5/document-metadata.html#the-link-element
Validation Issues: Updated October 27, 2017
Back in 2013, if you put a link tag within the body of the HTML document, it would not validate using validate.w3.org with rules based on HTML 4.01.
(You can try out HTML 4.01 versus HTML 5.0 validation at https://validator.nu)
On a first reading, the HTML 5.0 specification document seems to imply that link's should appear only in the head element of the document. However, if you validate using a HTML 5.0 validator, then the documents appears okay even if you have a link in the flow content.
The best explanation for this discrepancy may be as follows.
If you read the MDN documentation for the link entry (MDN Link entry), you see that if the link element has an itemprop attribute, then the link can appear in flow and phrasing content, thus, in the body.
This may be the reason why HTML 5.0 validators do not issue a warning even if the itemprop attribute is not present.
The itemprop is part of the microdata specification and is relatively new (read about HTML Microdata) and it is worth reading.
For the moment, one could add a link to a stylesheet within the body, but it is not clear what the advantages are.