RLM can take things so literally - the bible doesn't mention marriage licenses because there was no such thing. It does mention marriage and that living together unmarried is a sin. Part of the requirement to get married in the US is to have a marriage license. I believe the bible also mentions a requirement to follow the laws of the nation you live in, except where they contradict God's law - so bowing down and worshipping the king is right out, and you should allow yourself to be thrown into a den of lions for not doing that (c.f Daniel). But claiming you can't get married because the bible doesn't mention marriage licenses is complete BS - it's an admin thing, like travelling to the home city of your family in order to be counted for the census (see I nicely tied back to the Mary and Joseph thing there), I'm pretty sure that the bible doesn't set that out as a requirement under God's law.
As for the Mary and Joseph not being married, that is technically true. A couple would declare their intent to marry, and once that was all formalized they would move in as a married couple - it took time to arrange those big wedding ceremonies, and I'm guessing that whole census thing got in the way of having the party. It was also the case that if your betrothed fell pregnant and you weren't responsible, you could call it all off because she was obviously a woman of loose morals - an Angel did visit Joseph to tell him God would not be happy if he did this.
Bottom line RLM is a very selective when it comes to which of God's laws he needs to be following, and which he can ignore - but as for all the non-believers, they need to be following all of them, or else. Very bad example for a man of God to take.