Both sides of the coin
BBC under fire from ITV over awards sponsorship
Normally the BBC doesn't have problems with covering specific events (sporting or otherwise) that have a commercial sponsor, because avoiding any mention of the relevant sponsor would be highly impractical as well as upsetting various sports governing bodies who rely on sponsorship for a source of income.
Therefore the BBC can easily show sporting events along with any displayed sponsor logo(s) as long as they aren't displayed with undue provenance. The cameras are just there to report the event for the benefit of the licence fee-paying viewers, since there would be just as many business names displayed (for example) in a street full of shops.
However, what if an event specifically organised by the BBC - in this case the Sports Personality of the Year - had a sponsor? It's perfectly possible that covering the event wouldn't be a problem as long as it was done so in the same manner as if the event was organised privately by a sporting body.
Where things get awkward is the issue of the BBC receiving direct payments from a private sponsor, no matter how small the payments were and even if no profit was made from the transaction. As well as the ethics of deliberately sidestepping an advertising ban, there are accompanying issues such as that of sponsor selection.
But you could equally argue that a cash-strapped BBC is simply wreaking revenge on a government which has capped its licence fee as well as generally making life awkward for the BBC if not exactly being openly hostile towards the corporation.
Of course the BBC may have another loophole to exploit if things get tough - and arguably would have been the best and safest course of action in the first place - namely by delegating the whole event to its commercial division (BBC Worldwide) and getting them to find a sponsor instead.
More blog posts about: BBC, sponsorship