I don't think your sources support this conclusion. bovine spongiform encephalopathy (BSE) rarely passes the species barrier, but it is difficult, if not impossible to estimate what the rate is in the absence of mitigations.
Last but not least, there are huge uncertainties around the diagnosis rate of mad cow in humans. For example, a 2013 study (1) found that 1 in 2000 people in the UK now have Creutzfeldt-Jakob disease.
Based on this, it could be possible that transmission rates are very high if a human were to eat mad cow nervous tissue.
Also, these antibodies are not very selective for a given confirmation. Idk how this made it into the BMJ because standard in the PrP field is a protease resistance assay given the issues with Ab specificity.
I am not an expert in the field, but it seems relevant to consider latent or asymptomatic PrP expression when assessing how often it crosses the species barrier.