We've watched several videos. Have any of them come up with a message asking if you can send a caravan or cargo ship to their city? And you can get trade routes in the ancient era, but you can't get open borders until the Medieval Era. Do you propose only trading with city-states and your own cities until then?
And why would you allow anyone to send their caravans to your land anyway? I would never permit anyone else's trade units in my land if I could help it. That way they don't leach science and send religion to me. It's hardly worth the puny amount of gold you get from being a trade destination. Since both those things are possible, one must assume that you don't have control over incoming trade, only your own outgoing trade.
Additionally, Venice can "Purchase" science buildings in the puppets. And they can get science leach via trade routes, which they have twice as many of, if they are behind. So I don't think they will have too much of a deficit in science.