Besides, the original Intrepid was destroyed in "The Immunity Syndrome", so the Intrepid shown in TVH (assuming it was the Intrepid) was probably an entirely new ship with its own keel and everything.
I considered your observation, but why would an earlier registry (NCC-1707) be assigned to a refit in the 2280's when Star Fleet had already reached a higher number NCC-1764 (the Defiant) in the late 2260's?
I would assume that NCC-1707 would have been assigned to a ship commissioned not long after the Enterprise.
Further, and here I'm way out on a limb, we don't know that the Intrepid's hull was destroyed. The space amoeba was absorbing energy, correct? I'm not sure it was absorbing matter. The solar systems it had destroyed were still there, right? But devoid of life.
So perhaps the hull of the Intrepid (1707) was salvaged and refit.