I do not believe there is such a saying.
The reason one would not "pasken" (decide a case in law) by Tanach (alone)(besides the issue of Rabbinical injunctions), would apply equally to someone living in the era of the Tanach as it does to us in post-Talmudic times.
The Written Torah was originally given with the Oral Torah for a reason. It is obvious from reading the Written Torah alone, that it is too abbreviated and/or broad, to apply as rulings to individual legal cases by itself. However it is the firm basis and source of all Jewish Law.
The Torah says we must eat matzah (unleavened bread) on Passover. How much Matzah? We must not boil the Passover offering's meat in water. May we boil it in its own juices?
The Torah simply says we must "sanctify a priest (Kohen)." Does that mean we should give him the first aliyah on every Sabbath Torah reading? What if the synagogue needs money? May we auction off all aliyahs even to a Levi or Yisroel?
The Torah says we must put "judges in our gates". How many judges are needed in each gate to fulfill this? What's a gate? Does a judge get a salary from the town?
The Torah says we must not cheat each other. How much money is considered overcharging for a certain product?
The Torah requires witnesses for certain crimes and financial cases. What if a witness says: "I am not sure." or "I am almost certain." What if witnesses testify together to the same crime but one says he was wearing black and the other says he was wearing green?
The Torah says a thief pays double. What if the thief admitted to the crime and returned the goods? Does he still pay double?
If a man borrowed money with witnesses, but he now claims he paid the debt back without witnesses, is he believed against the lender who claims he never paid?
If two men came to court and each one claimed to be the father of a certain child, would you bring a sword like King Solomon did, or could you order a paternity test? Would another method be appropriate?
So a Rabbi who is paskening out of a Tanach by itself is flying blind. :)