You're using two different measures of "skew": endorsement (print media), and imbalance in coverage (BBC), and the headline conclusion depends on the content analysis of the BBC's coverage, omitting any consideration of ITV or Sky.
It seems to me that it would be better if you were able to rely on a single measure throughout. Loughborough's Centre for Research into Communication and Culture carried out content analysis of all major outlets, and found very different patterns (see, for example, Figure 4.2). In particular, they found that Leave newspapers were very much more Leave than Remain newspapers.
The two sets of data aren't comparable, because Loughborough don't disaggregate TV coverage by outlet. However, I suspect that if you were to weight the Loughborough figures by the average usage figures for each medium, you would end up with different conclusions.
In this case, I would struggle to support Civitas' research (carried out by News-Watch) over Loughborough. Neither report produces much in the way of inter-rater reliability, but since Loughborough researchers presumably have an interest in peer-review, they have an interest in defensible and reproducible procedures. News-Watch, on the other hand, seems to exist only in order to criticise the BBC.