Tether is a company issuing fiat IOUs on the Omni network. At the moment they offer USD and EUR IOUs and claim to be 100% backed by their assets with a proof of solvency. However, their terms of service don't inspire confidence:
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.
That being said, for a long time their USD price remained rigid in comparison to things like bitUSD. That is understandable - exchanges would accept it at par rather than trading it like any other asset.
A month ago, Bitfinex and Tether ran into some banking problems with Wells Fargo. The latter was acting as a correspondent bank and decided to block wire transfers between the crypto companies and their customers. Those wishing to cash their tethers out need to go through Kraken, which decided to take a ~7% premium for the service due to the market problems.
There are also some alleged shenanigans going around the actual use of tethers by exchanges and the BFX tokens (related article), but that's not directly relevant to our discussion at hand.
What this scenario shows is that there is that every currency needs a real market.
A long time ago, before central banks became prominent, each bank used to issue their own banknotes and the value of said banknotes would fluctuate based on the trust in the bank and so on. While that was a horribly inefficient system for the brick and mortar world of retail, wasting countless hours on currency conversions, individual counterfeit measures and so on, it could work really well in the digital space.
A dollar from one bank or exchange is not worth the same as a dollar from another. A faster, more efficient exchange would have their tokens valued more favourably than a slow, clunky one. Eventually, the market would settle at some price that would indicate the level of confidence or quality of the exchange and that metric would be clear for every customer to see. We had that with the final days of MtGox.
At the current time, the only place we can see a clear market like that is Ripple - you can actually trade USD IOUs from two different gateways for one another (at the time of writing, the exchange rate between Gatehub and Bitstamp USDs is about 1.11). While each gateway accepts their own tokens at par and allows you to withdraw the USD to your bank account, the price is driven by market makers that decide what premium to charge. If someone else finds a way to close that gap, they have a chance to make some money and bring the market into a more realistic exchange rate. In the end, the market decides what each IOU is worth, not some exchange.
While the current Wells Fargo problem is an important issue for Tether and Bitfinex, it is an important example for why we need a liquid market for all tokens, even those denominated in fiat. That and why correspondent banking is a thing that needs to be replaced by cryptocurrency networks.
A dollar is not a dollar is not a dollar.