It is worth mentioning that while it might be tempting to set your offsite to something higher than you actually have, by doing so you would most likely end up earning less than you would otherwise.
I'm not sure that's accurate. Most likely the site will continue to profit overall with swings up and down along the way. It's possible that there will be a downswing large enough to cause a 2:1 leverage investor to lose their position, but "most likely" it won't happen, and so "most likely" the 2:1 leverage investor will do better than an investor with no leverage.
Or am I missing something?
I'm not saying there's no risk, but it's more like a small risk of catastrophe than a big risk of small loss.
As an analogy, a risky home owner might decide not to buy fire insurance. You would want to warn them that it's a risky move, but to tell them that they will "most likely" end up worse off that someone who did buy the insurance wouldn't be correct. Most homes don't burn down, and so in most cases paying for insurance is a waste of money.
I recommend only investing offsite if you actually have the funds and are prepared to deposit them quickly in order to avoid a margin call if necessary.
Or if you understand the risks, and want a higher risk, higher reward investment, right?
I'm also a bit confused by these two apparently contradictory statements you made:
Leverage of 2:1 means that your onsite investment can "control" a total investment twice its size. In other words, your offsite can be up to the size of your onsite (10 BTC in your example).
and:
Assuming your onsite is 10 BTC, your offsite is 20 BTC
If 2:1 means offsite amount is same as onsite amount, and 2:1 is the limit, how could he have 20 offsite and only 10 onsite?