Just to satisfy your curiosity, yes, I do believe it was an Argentine settlement. My reasons are the same that have been provided to you over and over and over: 

 *Vernet was an Argentinian citizen. His personal life was committed to Argentina. He had a daughter on the islands whom he called Malvina. Despite his French origin, German birth and American upbringing, he signed his name in Spanish. 
 *His political appointment was made by Argentina. 
 *The currency unit used was Argentina's. 
 *The justice system prevailing was Argentina's (e.g. the fishing ships seized were taken to Buenos Aires, not London, to stand trial). 
 *The diplomatic coverage was provided by Argentina (e.g. after the Lexington raid). 
 *The language used was Spanish. 

 Of course, you're right that there are other circumstances too long to explain, and that's why the scholars agree to summarize the situation saying that it was an Argentine settlement, or even colony. And here in Wikipedia we must closely follow what the scholars say. When we tell the whole story, we stick to the whole story told by them. When we summarize, we stick to their summaries. But taking their whole story and producing a summary significantly different from theirs is plain WP:SYNTHESIS.