No, they only need to produce an official email that she failed to submit from one of her contacts. Hillary has no capacity to delete the emails on other peoples servers. Rivals just want an opportunity to go fishing in her private mail.
She has the right to filter out her private emails. There are political rivals that are eager to get into her private mail for very political reasons.
Indeed, she should have realized that there were political pitfalls, it was inappropriate and she can surely see that now, but she did not break the law. http://thehill.com/policy/technology/234487-hillarys-emails-not-technically-illegal
“There was no prohibition on using a non-State.gov account for official business as long as it was preserved,” State Department spokeswoman Marie Harf said on Tuesday.
Jason R. Baron, a former director of litigation at the National Archives and lawyer at Drinker, Biddle & Reath, said the authors of the law had not anticipated that such a prohibition would be necessary. The Federal Records Act “assumed that high-level officials will use government-approved record keeping systems for the transaction of government business,” he said. “So while it is not illegal per se to use a private email account like Gmail, it is highly unusual for a high-level official to solely use a private account for the transaction of government business."
Off topic, but you are far from alone in misusing that phrase and it is one of my pet peeves. The original phrase was "Hoist your own petard", which means "do your own dirty work". A petard was a medieval shaped charge consisting of a bell-like small cannon without a projectile. It was used to blow open a fortress gate by explosive force alone and it was effective at that. The drawback is that to use it someone had to go out and drive a hook into the gate and then someone had to run out with the petard, hoist it onto the hook, light the fuse, and run back, all under fire from the defenders. It was usually assigned to strong, brave young men who had a high mortality rate. But Shakespeare twisted the phrase, as he did so many, and in modern usage it has come to mean being blown up by their own bomb or "to fall into ones own trap".