So even valid secular marriages can't be split by the state?
"Can" vs. "shall". Can someone rob a bank? Yes, someone can rob a bank. Shall someone rob a bank? No, thou shalt not steal.
Can the state split a secular marriage? Yes. Shall the state do this? No. The fact that the state does it only makes it technically legal, it doesn't make it right. For proof, look at all the other kinds of legalized sin.
That's the essence of what SimpleMan, Nadir, HeavyHanded, and a few of the Anonymous posts are saying.