Ah yeah, on second thought, of course she would like Cloud carrying her. I mean, who wouldn't like their crush doing that right when they could do with the help?
Though it's still embarrassing as hell I would think.
As for why the chopper didn't shoot her, maybe they didn't see the grenade and didn't think she was a threat. Or maybe they shot her but her HP wasn't down to 0. Or maybe they were just dumb. I don't know.
One issue I have with that chapter's writing, is that it it has too many issues like that which make little sense, even for an FF title. I get that they do that in favor of cool cutscenes, but still...
Why were the party taking cover behind a bunch of explosive tanks when they reached the top? Why did Barret shoot the chopper instead of Reno? And to top it off, the Whispers showed up. Ugh. Wait, no that's not the end of it. Cait Sith too.
It's still one of my favorite chapters though. Overlooking the finer details, by bringing everyone back to fight in one place (the main party, Avalanche and the Turks), while the one truly responsible for these events watches from the comforts of his office, I think they nailed the overall sense of frustration and futility.