You were both wrong. 
And simultaneously, too!
In case you haven’t seen it, the latest bit of Argentinian propaganda is about as pathetic and childish as it has got:
Don’t they realise that every time they do something like this they just strengthen the resolve of the Brits to just not give in? It is almost as if they don’t actually want the things.
Looks like Argentina likes to shoot themselves in the foot(again)…or cut their noses off (to spite their face).
I guess they are telling the world: “don’t invest here-we’ll steal from you…and don’t DARE drill for oil-we’ll throw you out”.
I cannot imagine any government being so stupid as this.
And the thing is you can take that commercial (made by a New York ad agency, incidentally) two ways. Clearly the intention was “here’s a proud Argentinian athlete, running around an island occupied by los Ingleses”. But from another perspective, it’s “Argentinian guy for some reason does his training in place that is obviously culturally British.”
That’s, like, an Iraqi Information Minister press conference level of lame.
My favourite comment to that video:
“Doesn’t bode well for his Olympic prospects. Can only manage 1 press up.”
I wonder if he and the film crew were in the Falklands legally.
Did they just row to shore and film really early on a Saturday morning before everyone was up and about?
It explicitly states that it is Argentinian Soil.
“Para competir en suelo inglés … entrenamos en suelo argentino”
I’m sorry, but there is only one way to take that.
Meh. Just follow it up with British naval exercises in Argentine waters, Operation We Can All Play Silly Bastards If You Like.
That’s just an end caption, in case the home audience didn’t get the point. Which I wouldn’t blame them for, because the actual film still seems ambiguous to me.
So your opinion is that it can be taken two ways as long as you ignore the bits that make it completely unambiguous what the film was about. Got you.
As a continental European, I think the latter would be a wonderful idea.
On topic: I live in one of those many countries that may be argued to have a “bleeding border”. We have learned to live with it and move on. I cannot be particularly impressed by the claims that some Argentinians believe to have on the Falkland Islands.
Wow, calm down. Yes, if you ignore the caption, which is the only bit you mentioned, the rest of it can be taken two ways.
Isn’t jumping up and down on a British war memorial thirty years after beginning a war you lost with them a little much? 
It’s either a drastic misunderstanding of the nature of the British, or a deliberate way to declare they no longer want the islands. Either way, it’s an action which helps ensure they’ll never get their way.
The point is that the makers of that spot do not consider the good will of the British or the Islanders necessary for the islands to be returned to Argentina, they think that UN resolutions and economic pressure from the continent will be enough for that. I think they are sorely mistaken but that’s the way they think.
Also to them is self-evident that the islands are Argentinian, their way of thinking is very similar to the American “Manifest Destiny” advocates in the 19th century, they are CERTAIN that the islands are Argentinian and are completely sure that eventually they will because that is what is just and correct.
Again I think they are sorely mistaken and are just ensuring that any realistic foreign policy goal Argentina could have in the area (like, for example, a co-participation agreement with respect to the area’s oil profits) are delayed 10 or 20 years or simply made unreachable.
Look, the USA didn’t just take some islands from my country, they took the whole damn thing.
We just sucked it up and got some of Ours elected President.
They should learn to deal with it.
Again, you’re being wise after the event. There is no indication from the film that one of the sites in the film is a war memorial.