They're not saying that larger deposits will take 1 confirmation. They're saying that they will take at least 1 confirmation.
How can they do this and cover themselves from double-spending?
Sure, doing this increases the risks of double-spending. However, that might be an acceptable risk. They may have done the math and figured that the additional business they get is worth it.
They might be doing it to distinguish themselves from the bajillion other exchanges out there.
Also, they're charging a fee of 3.7%.
Edit: Clarification
With ShapeShift, what you see is what you get. The exchange rate shown is exactly what you'll receive, minus only the "miner fee."
There is no exchange fee, or service fee.
This is true, but the spread is noticeably higher than on other sites.
I arrived at 3.7% by taking the BTC -> LTC exchange rate and comparing it to the LTC -> BTC exchange rate.
1.00 BTC = 137.1636 LTC
1.00 LTC = 0.00685688 BTC
If you multiply 137.1636 and 0.00685688, you get 0.9405. This means that if you exchanged 1 Bitcoin for Litecoins and back, you would have 0.9405 Bitcoins left. (Ignoring transaction fees.) This is a change of 5.95%. Divide that by two, because you'd only exchange once.
This gets you 3.0%, which is different from my original calculation because the prices on ShapeShift have changed since then.
So there is a fee, but it's baked into the price they show you. On the other hand, if you're exchanging less than 0.33 BTC, the fee is lower than what BTC-E would charge you.