I think Liz Cheney's the one "distorting her views". In 2009, she fully supported her father and sister's position, and was all for the federal government promoting gay marriage:
“Q. How do you feel about the California Supreme Court's decision [on Proposition 8], and what do yo think the Obama administration should do on the question of same-sex 'marriage'?”
“A. Well, look, I think, you know, my family has been very clear about this, that we think freedom means freedom for everybody."
“I applaud the State Department decision to extend benefits to same-sex partners around the world. I think it's wrong to discriminate in those relationships based on somebody's sexual preference.”
“I certainly would not like to see a constitutional amendment, as was suggested in the last administration, banning it.”
No she didn't, she said it is a state issue...........