Quoted from the Opera for Android FAQ:
"Can I download media files, such as YouTube videos?
Yes. Long-press the content you wish to download and select Download. Please note that many websites only offer media content as streams that cannot be downloaded."
Right, firstly, YouTube was probably only given as an example (as YouTube is probably one of the most well known media sites) and does not specifically mean you can actually download YouTube videos. Secondly, the second sentence qualifies the first part, as YouTube is a media streaming service that does not offer media files for download in-line with parts 'L' and '9.1' of its TOS.
Part L:
"you agree not to access Content or any reason other than your personal, non-commercial use solely as intended through and permitted by the normal functionality of the Service, and solely for Streaming. "Streaming" means a contemporaneous digital transmission of the material by YouTube via the Internet to a user operated Internet enabled device in such a manner that the data is intended for real-time viewing and not intended to be downloaded (either permanently or temporarily), copied, stored, or redistributed by the user."
Part 9
"YouTube content on the Website
9.1 With the exception of Content submitted to the Service by you, all other Content on the Service is either owned by or licensed to YouTube, and is subject to copyright, trade mark rights, and other intellectual property rights of YouTube or YouTube's licensors. Any third party trade or service marks present on Content not uploaded or posted by you are trade or service marks of their respective owners. Such Content may not be downloaded, copied, reproduced, distributed, transmitted, broadcast, displayed, sold, licensed, or otherwise exploited for any other purpose whatsoever without the prior written consent of YouTube or, where applicable, YouTube's licensors. YouTube and its licensors reserve all rights not expressly granted in and to their Content."