Why should there be any "problems" (and i infer you mean, in this case, deficiencies) in either system? Certainly in the UK educational system individuals are taught to consider differing entities on their individual merits. The UK and EU view professional studies (such as Medicine and Law) as undergraduate pursuits, whereas the US as postgraduate disciplines; neither practice is without flaw.
I think very few academics would view the US MD degree as anything more than a professional qualification; any bozo can study medicine - the difficulty is with getting a place at medical school, once obtained, only sheer motivation and perseverance of the individual will equate to qualification; medicine isn't a conceptually challenging discipline. To study at a doctoral level demands an entirely different set of personal qualities, aptitudes and skills in addition to those for medicine alone.
Medical training in Europe is traditionally undertaken at the undergraduate level, Italy is no different; the "Diploma di laurea in medicina e chirurgia" or Diploma of graduate in medicine and surgery is a professional qualification pursued at the undergraduate level, it is NOT a doctoral degree, its literal translation of 'diploma of graduate in doctor of medicine and surgery' simply refers to the fact that the particular individual is a graduate in medicine and surgery much in the same way as an MBBS-holder is a graduate of the degree of Bachelor of Medicine, Bachelor of Surgery. Graduate-entry medical programmes in the UK, incidentally, do not confer 'postgraduate' qualifications to their graduates, they are, like non-graduates, awarded the MBBS/MBChB/etc.
The fact that you've written a thesis is irrelevant; medical students in the UK who intercalate - either as a mandatory part of their studies or by choice - are compelled to spend an additional year undertaking independent lab-work, field-work, or literature-based research in a specific area of medical science culminating in a dissertation and viva voce, yet they are not conferred a doctoral qualification. In fact, most undergraduate students (whatever the degree subject) are required to complete a dissertation in their final year before being allowed to graduate; they are conferred 'honours' with their BA/BSc in recognition of this - oddly enough, the MBBS is not an honours degree, though students can obtain honours by spending an additional year intercalating, in which case they graduate with two degrees.
This is essentially a dispute about terminology; a medical degree is a medical degree, whether it's an MBBS or an MD, neither of which are true doctorates in the academic sense.