Because the adverb attracts a verb (that is why it is called "adverb"). An adjective can stand in place of a verb (Az orvos okos), but the adverb defines/modifies/clarifies how the verb is to be interpreted. This concept is not different from that in the English: https://en.wikipedia.org/wiki/Adverb
Unfortunately it is wrong, indeed. 'That doctor is alone.' is not equivalent to 'The doctor is alone.' in English, either. The distinction can also be expressed in Hungarian:
Az orvos egyedül van. = The doctor is alone.
Az az orvos egyedül van. = That doctor is alone.
In the second pair, 'That' is a demonstrative adjective, and its function is equivalent to 'Az az' in the Hungarian version. Note that in the Hungarian sentence the first 'Az' is a demonstrative pronoun, whilst the second 'az' is a definite article. To express the English demonstrative adjective, we need to use both 'az'. Similar constructs are quite common in German as well.