"The Street put out a release today saying that QRE goes ex-dividend tomorrow."
Yes, it does.
"Yet in the company press release they say that the ex-div date is Jan 14."
No, they don't.
What gives is that you're seeing things that aren't there. The company's press release doesn't say the ex-date is the 14th. It doesn't even mentions the ex-date at all. It gives only the payment date and the record date. And since it gives the record date as the 13th, it looks like you're inferring the ex-date will be the 14th. It won't. The ex-date is the 9th. Ex dates occurring one business day after the record date is the way mutual funds work, not individual stocks.
Not true, is it? Haven't checked my QRE K-1s but I assume they had positive income like most E&Ps. You pay tax on the numbers in boxes 1-11 and if they are positive then it's not tax free, or even fully tax deferred.