While it is true that the remains of the settlement were only found fairly recently, there were other Norse artifacts found in N.A. long before that. Buttons in New England, pre-Columbian iron artifacts in N.E. America, butternuts way south of where they should be, etc. That was what led archaeologists to search for Norse settlements.
People just can't move around without leaving trash wherever they go. We can't go someplace new without picking something up. If we come across somebody who has something that we don't, and we have something that they don't, some sort of trade inevitably occurs. It always has.
The Norse hardly traded with the locals at all (and were only driving longboats), and yet stuff that they made has shown up hundreds of miles away from their settlements. The Chinese supposedly launched a trade expedition with 450' ships, with the specific purpose of establishing new trade routes. They left nothing in North or South America, and they brought nothing back with them.
All that way, with thousands of men, and they never even used the little boys room? ;-)
So what you're saying is, we need to look for the remains of Chinese outhouses... ;')
I don't think too highly of Menzies' ideas (or this topic's derivative book). There's a recent topic about an upcoming dive on a 600 year old Chinese wreck near an island off Africa. The Chinese made it to western Africa, and were not the first to do so, so at least that has a shot of being worthwhile.
In ancient times, the Chinese sent a ship to Mesopotamia, an embassy to the Roman Empire, and just missed (Trajan died right after completing the drive to the Persian Gulf, and his successor Hadrian withdrew). The Han court records show a Roman representative (arrived by sea) during the reign of Marcus Aurelius. Probably most of the contact between east and west in antiquity was through middlemen, but there's been some evidence (like the Han court record) of direct contact.