Funny!! Who told you that TN holders cannot get married in USA .

if you want to lie her ... that's another story.

also she can keep using TN after you two get married.

Just like the case that many students, entered with F1 visas initially, get married when they study/work in the USA, TN visa holders may get married while they work in the states too. Things may change, and these cannot be considered as frauds.