Dutch to German Law/Patents Law: Contract(s)

I translated "huurovereenkomst" with "Mietvereinbarung" ("lease agreement") as it is said in the dictionary.

My client's proofreader insisted that "Mietvereinbarung" is not possible and therefore a mistake, it should be "Mietvertrag" according to them. However, "Mietvertrag" should be the translation of "huurverdrag"or "huurcontract" ("lease contract").

I checked on a search enginge and received approx. the same amount (4M) matches for "Mietvereinbarung" as for "Mietvertrag".

Is there any good reason why the client insists to mark "Mietvereinbarung" as a major mistake and thus reject the whole translation?