It doesn't use di vedere in the subordinate clause because the subject of that clause is un medico. The literal meaning of the clause is "that a doctor sees you". As the two clauses have different subjects a relative (subordinate) clause starting with che and using the subjunctive is required.
"Hai bisogno che un medico ti veda." Doesn't this say "You need a doctor to see you," without unnecessarily placing the direct object at the end of the sentence ("for emphasis" as I'm regularly told is the excuse for this confusing construction)? And if we're getting down to simple, straightforward English, doesn't "Hai bisogno che tu veda un medico" "You need to see a doctor" make the most sense?
I suspect that in Italian when you go to a doctor it is for the purpose of him seeing you rather than you seeing him. Thus, the construction of the sentence. In English we simply use the phrase of going to see the doctor without thinking much about what a patient gains by literally (and merely) seeing the doctor.
Exactly. I think most of the posts on this discussion are missing the important point that the normal English expression is for you to see a doctor but the normal Italian expression is for the doctor to see you. DL is as usual too literal so we should just ignore their computer and learn this interesting reversal of thinking.
Anyone who has a phd can be called a doctor regardless of which subject they studied. Dottore in Italian does mean doctor but only refers to a professional person, and a phd is not specifically required. In English, a doctor is usually understood to be a medical doctor, whereas in Italy, if you want to see a medical doctor, you would have to say medico or there might be some confusion.
IF the sentence were "you need to see a doctor." No subjunctive would be necessary,right? "Hai bisogno di vedere un medico." But since the need for you is that the doctor see you, 'che...medico' acts as a subordinate clause being used as the direct object of your need. Right?
Your sentence was likely marked incorrect because "that" is not used in this way in English. Although similar structures in other languages would use a conjunction, in English, "I/you/he need/s" is not followed by a conjunction such as "that", and including it would make a sentence incorrect.