Could an oil conglomerate convince a country that they own the highly-debated Shatney islands in order to extract oil from the islands?

This is a complex question that involves several factors, including international law, diplomacy, and corporate influence. Here's a step-by-step breakdown:

1. Establishing Ownership: The first step would be for the oil conglomerate to establish ownership of the Shatney Islands. This could be done through a variety of means, such as purchasing the land from the current owner, or through a legal process if the ownership is disputed.

2. Negotiating with the Country: Once ownership is established, the oil conglomerate would need to negotiate with the country in question. This could involve convincing the country's government that the conglomerate has the right to extract oil from the islands. This might involve legal arguments, economic incentives, or political pressure.

3. Obtaining Extraction Rights: Even if the country is convinced of the conglomerate's ownership, the company would still need to obtain the rights to extract oil. This could involve further negotiations, and possibly the payment of royalties or other fees.

4. Overcoming Opposition: There may be opposition to the oil extraction from various quarters, including environmental groups, local residents, and other countries. The conglomerate would need to manage this opposition, which could involve legal battles, public relations campaigns, and further negotiations.

5. Extracting the Oil: Finally, once all the legal and political hurdles are cleared, the conglomerate could begin extracting oil. This would involve significant logistical challenges, including transporting the oil and managing the environmental impact of the extraction.

In conclusion, while it's theoretically possible for an oil conglomerate to convince a country that they own a disputed island in order to extract oil, in practice it would be a complex and potentially contentious process.