"no it's just wrong" :-)
In your reply 新しいの, the の means "one", as in "the new one". This の behaves like a noun and the i-adjective directly modifies this.
背が高いの would be grammatical ("the one who is tall") though I think it would be very rude and non-standard.
背が高い方 would be grammatical ("the person who is tall"). Again the i-adjective directly modifies the noun.
背が高いの方 is not grammatical. This の cannot be the one that means "one" because you cannot put two nouns next to each other (の方). Also "the tall one person" sounds weird even in English. In the other way of using の, XのY, X and Y must both the nouns/noun phrases and you have 高い/背が高い in the X position which is not a noun/noun phrase, so it must be ungrammatical.