DaveEllis, I think to be fair to
Elio the concern raised is not so much one of bias but of promotion.
Promoting the profile of the racing Brits in British broadcasts ("bias" if you will) has been around since the days of radio; from Clark & Graham Hill, to James Hunt, to Mansell, to Damon Hill, to Coulthard (to an extent) and certainly to Lewis. Murray was never impartial to an individual; witness the famous "lump in my throat moment" over Damon Hill. If you've never watched a French broadcast, especially in the days of works Renault cars, driven by Prost, fuelled by Elf (and later shod by Michelin), then you're in for a shock!
Where commentators being biased for these drivers is based on themes of nationalism, I believe the concern is that Coulthard will be biased towards (i.e. promoting the interests of) Red Bull which is a commercial organisation. The team exists because a soft drink manufacturer wanted a cool, high-profile method of selling more of his soft drinks so he can make more money. Coulthard is being employed by a public body (the BBC), his salary coming from the licence fee drawn from our pockets, and is still singing to the tune of a reported £4m annual retainer as RB consultant. That's where I reckon most people are getting their knickers in a twist over a possible conflict of interest.
I don't know if Coulthard is therefore "biased" in that way. He's been with the BBC 2 years now and has had plenty of time for this vexed question of commercial interests to raise its ugly head. It's only getting exposure now because he's becoming a co-commentator rather than a pundit. I'm quite willing to wait and see.