The BMJ, ironically, is prone to publishing articles that make unverified claims without making clear rather significant conflicts of interest.
Infamously, they published a largely spurious article which claimed that UK govt cuts had killed hundreds of thousands of people, they failed to make clear several aspects of the data that didn't support their conclusion which ofc was that doctors should get more money, they also failed to mention that one of the authors ran a company selling stuff to the NHS that was linked to the conclusions or that the lead author of the paper had no statistical training.
Unfortunately, life is like this. Doctors would prefer that people just listen to them, they are very serious people after all, we should believe everything they say. Most fact-checking services in the UK have a ludicrously political bent, they pick whatever facts and sources support their argument. In practice, they are just attempting to stop all debate about a topic. Life is messy, people will have different opinions even if they acknowledge the same facts, proof is often messy and unclear (if you look at some of the forecasts for Covid this year, just ludicrously wrong and all errors in the same direction...we need criticism, we need debate...afaik, only one publication has actually highlighted all these forecasters who dominate the media making consistently bad forecasts...where are the fact-checkers now? Too busy hunting down shadows on Twitter.). Deal with life as it is, not life as you wish it was (again, doctors in the UK are more guilty than anyone in civil society of this error, their lobbying/political power is immense, their view is: might makes right).