The defence is linked to Art 5(1) of the Copyright Directive[1], which states that where a reproduction is temporary, incidental or transient. it will not be considered to be an infringement.

A download would classed as anything that didn't satisfy those conditions. So if you're storing something for the purposes of making use of it later it would fall outside the exception as it would not be temporary or transient.

Technically your browser downloads content of course, but provided the content is only viewed whilst you are in the browser and not retained following the end of your browser session (or were merely retained in your cache), this would not constitute a download for the purposes of putting a user outside the exception to infringement under Art 5(1).

[1] http://eur-lex.europa.eu/LexUriServ/LexUriServ.do?uri=CELEX:...