So BBC Sussex using air time, lets say, to tell you that they have cricket or football commentary for the Albion is hypocrisy because the BBC is funded by a licence fee and they happen to have sensible guidance about how prominent commercial products should be mentioned on air.
Yes. They can. Although its a balance...
"[The BBC] needs to be able to reflect the real world and this will involve referring to commercial products, organisations and services in our output. However, we must avoid any undue prominence which gives the impression that we are promoting or...
Tag are a new Premier League sponsor
https://www.premierleague.com/partners/tag-heuer
BBC Sport and its use of logos in this way is explained via
http://downloads.bbc.co.uk/bbctrust/assets/files/pdf/appeals/esc_bulletins/2013/mar.pdf