Of course they will. But their incentives are slightly different so combined with corporate media and 'independent' media they can paint a more accurate picture. Freedom of the press is very important but in a capitalist system you should also have media outside direct capitalist influence.
That being said looking at the BBC and NOS the idea that it's used for propaganda doesn't seem all that major. If you have laws about freedom of the press then the government's ability to dictate public news is limited. The government might pay for public news but they don't dictate what it says. Of course in reality it is more complicated and public news is not likely to attack the government directly but that's what corporate news is for.