You might be able to store them on a local wallet (probably available at Tether's website), but like any other "fiat storage" it is subject to third party risk. In this case the owner of Tether. If, say, the USA didn't like what Tether is doing, and seized their bank accounts, how much is that USDT going to be worth? It'll dump hard.
Something close to that already happened actually. According to Tether itself:
Since April 18, 2017, all incoming international wires to Tether have been blocked and refused by our Taiwanese banks. As such, we do not expect the supply of tethers to increase substantially until these constraints have been lifted.
https://tether.to/announcement/And who said that you having Tether means that you have USD, and that you will always be able to redeem your Dollars when you need it? I honestly wouldn't trust my money on them.
PURCHASE AND REDEMPTION OF TETHERS: The Site is an environment for the purchase and redemption of Tethers. Once you have Tethers, you can trade them, keep them, or use them to pay persons that will accept your Tethers. However, Tethers are not money and are not monetary instruments. They are also not stored value or currency. There is no contractual right or other right or legal claim against us to redeem or exchange your Tethers for money. We do not guarantee any right of redemption or exchange of Tethers by us for money. There is no guarantee against losses when you buy, trade, sell, or redeem Tethers.
https://tether.to/legal/