This equation is extremely reductionist in ways that end up giving the Saudi government's stance as much merit as possible, while denying it to the UK every step of the way. The implication of what you're saying is that the structure of the government and the precise way in which it owns a state media outlet doesn't really matter, if there's any ownership then it's a propaganda mouthpiece regardless of all other circumstances.
But as far I can see, authoritarian states tend to have a direct path from their governments' sacred opinion to the eyes and ears of the people, there are levers of direct influence within their media industries that let them directly dictate what the journalists will pretend to report on. One can debate back and forth about how the BBC may suffer from the biases of its British writers, implicit pressure from their government, individual cases of bias and even attempts at government overreach, but despite all of it, none of these infractions would rival even 1/10th of what countries like Saudi Arabia or Russia do with their media. Despite all of their countless issues, the UK still values independence far more than what the Saudis could even dream of. Moreover, the BBC is implicitly checked by having neighboring media outlets with no government ownership, while the countries I listed exercise degrees of total control over the entire industry.
The BBC may in individual instances be biased towards the current sitting government or pro-British views or whatever, but it is not a blind mouthpiece like these other countries. It's not simply a difference in preferring one ruthless government narrative over another.