There is just not enough liquidity on Tether for it to follow the USD so closely. It has been very difficult to sell Tether for USD to Bitfinex AKA Tether over the past year. For awhile, any normal user had no option to withdraw USD from the platform at all. Their banks were completely shut off from the system.
You can argue there were people who were on the inside with Tether / Bitfinex and were able to sell Tether to them. I think there may have been some individuals / organizations that had the ability to send and receive fiat to Bitfinex, but I highly doubt they do enough volume to fully stabilize Tether 1:1 to the USD.
Look at Bitcoin over the past 1-2 years. It is completely common for it to trade at a 3-5% spread between USD exchanges. Don't get me started on exchanges in other fiat currencies. The spreads have been known to reach 10%+. These spreads can also be arbitraged by anybody, but they still appear. So I strongly doubt that Tether is a special case.
If Tether was trading on a real market, it would certainly not follow the price of USD 1:1.