Is this a ridiculous argument: "If the land contains Chinese-made products many thousand years ago then that land belongs to China's territory"?

Question

Ok, let see this argument:

If A then B, A therefore B

Look at the picture below, do you see the red line? & do you see many small islands inside the red line?

For thousands years these islands are the place that many fishermen in SouthEast Asian countries like Vietnam, Philippine, Brunei, Malaysia come there, catch fishes & make a good living on them. However, the China from nowhere suddenly claimed that all these islands belongs them because they found many "Made-in-China products" in these lands so the China assumed that there are Chinese people living there & thus these lands are the China's territory.

So their argument:

"If the land contains Chinese-made products many thousand years ago then there were Chinese people used to live there,
 if Chinese people used to live there for thousands years then that land belongs to China's territory"? 

Is that a ridiculous argument?

Answer 1

The question appears to be about sovereignty, spheres of influence and terra nullius; and these are all topics in political philosophy as it deals with the relations between states and opposed to within a state. So one can think of this as question of international relations or geopolitics.

The premise is a ridiculous one,and is unlikely to be used by serious diplomacy on resolving the disputed territorial status of the The Spratly Islands (Chinese name: Nansha islands, Vietnamese Name: Quần đảo Trường Sa, Filipino Name: Kapuluan ng Kalayaan).

There are already small military occupations by China, Taiwan, Vietnam, the Phillipines and Malaysia. Additionally the Kingdom of Brunei claims an exclusive economic zone in the south of the island.

Early cartography by the chinese show that

Ancient Chinese maps record the "Thousand Li Stretch of Sands" (Qianli Changsha ) and the "Ten-Thousand Li of Stone Pools" (Wanli Shitang) which China today claims refers to the Spratly Islands. The Wanli Shitang have been explored by the Chinese since the Yuan Dynasty and may have been considered by them to have been within their national boundaries. They are also referenced in the 13th century, followed by the Ming Dynasty.

Whereas the Vietnamese showed

A Vietnamese map from 1834 also combines the Spratly and Paracel Islands into one region known as "Vạn Lý Trường Sa", a feature commonly incorporated into maps of the era ‒ that is, a combination of half of the 2 aforementioned Chinese island names, "Wanli" and "Changsha". According to Hanoi, Vietnamese maps record Bãi Cát Vàng (Golden Sandbanks, referring to both the Spratly and Paracel Islands) which lay near the Coast of the central Vietnam as early as 1838.

But its also admitted that:

Despite the fact that China and Vietnam both made a claim to these territories simultaneously, at the time, neither side was aware that its neighbor had already charted and made claims to the same stretch of islands

Answer 2

The suggestion that the presence of Chinese products implies Chinese occupation is unsound. There are other possible reasons for the presence of Chinese products other than that Chinese people lived there, such as trade or abandonment.

That is not to say anything about the political statement about whether or not China has a claim to those territories, only that that particular argument does not compel such a conclusion.