I remember reading a fic that called Clint and Nat 'the silent avengers' and I like that, because there is no way SHIELD would have let them do press or anything. So yeah, there would have been speculation about their identities, I think.

Also, would Nat's info dump mean their relationship status was made public? (assuming they're together) Or do you think they managed to hide it from SHIELD? Because I think there would definitely be rumours, but then there might also be Nat/Steve rumours, and occasionally they get out the popcorn and sit down to read the more outrageous ones.

I think gossip sites probably spread rumours about Natasha and every other Avenger, because she's the only woman. *sigh* I can imagine Clint seeing her on her laptop and saying "So who are you cheating on me with this time?"

Natasha: "I had a wild night with Thor and Bruce, apparently. You're angry, as evidenced by this photo."

Clint: "You mean the photo of me getting pissed because someone shoved a camera in my face the moment I left the door?"

Nat: "The same."

Ugh, gossip sites. Steve probably has a "secret grandchild" popping up every other week.

I think the public attitude towards them probably did change after the SHIELD collapse. After NY, they were probably just viewed as part of the awesome Avengers who saved everything...I'm sure not everyone thought highly of them or of the Avengers in general for various reasons, but we saw in ep 1 of Agents of Shield that there were Hawkeye and Black Widow action figures.

I am very curious what the dump on the net could contain and how the public would view it. Natasha for example...obviously she killed people and Clint too has a criminal past...and even with SHIELD some people might not be thrilled with their kill count. Is it detailed, who they killed and why? Is there anything about how Natasha was trained as a child to be a killer? I think that info might make people very angry with her, or make people feel very bad for her.

I feel like in the MCU, the public probably DOES spectulate about their private lives. I can see folks pairing Natasha up (and the guys too) with the other Avengers.

there'll be some people wanting their heads on a platter, and other people saying that they were working for the good of the country/world
but Nat's past in particular could definitely cause trouble...

... and at some point after New York, some investigative journalist will come across those guards at the research facility having been killed by arrows and start to wonder just how the bow and arrow became the latest weapons fad (because wasn't that one Avenger, the one who was on the rooftop and outside iPhone range, using a bow and arrow too?).

And then the conspiracy theories will start -- maybe SHIELD staged the whole thing? Those theories will regain currency when Natasha does her info dump and it turns out she once fought for the Other Side...