I think the debate is more complex than this polarisation may suggest. The article defines the 'medical model' as denoting "the idea that mental health problems are best understood as 'illnesses like any other'". Even though there may be people that define and apply the 'medical model' in this way, I think most people do recognise a difference between mental and physical illness. Again, some people may want to minimise the difference between mental and neurological illness (eg. see previous post), but psychiatry is a separate speciality from neurology. The reason for this is that the two specialities deal with different kinds of medical problems. Those that want to work towards merging neurology and psychiatry at least realise we have not got there yet.
The article references Mary Boyle to define the 'psychosocial model' as a "framework that removes biology from the position of privilege in favour of a focus on the relational, interpersonal and social contexts of distress". This is fundamental to a critique of the biomedical model in that we need psychosocial explanations of mental health problems rather than reducing such problems to brain disease (see eg. previous post).
What worries me is the way the 'biopsychosocial model' is seen as a way of reconciling the 'medical model' and 'psychosocial model' in the senses defined by the article. Engel's biopsychosocial model is is fact the same as the article defines as the 'psychosocial model' (see eg. previous post). True, the people that the article references in relation to the definition of the 'biopsychosocial model', such as Allen Frances (see eg. previous post) and Robin Murray (see eg. another previous post), do use the term in an eclectic way. But this was not what Engel meant.