Not quite - the current legislation[1] is that you must have a TV license if you watch/record live TV (however you do it - online, with a TV, etc.), or if you use the BBC's iPlayer app/site.
You do not require a TV license if you have a TV but do not use it to watch live television (e.g. using it for YouTube/Netflix apps)
You do not require a TV license if you have a TV but do not use it to watch live television (e.g. using it for YouTube/Netflix apps)
1: https://www.gov.uk/find-licences/tv-licence