The Short Version
This claim is false on two counts. First, common-law marriage is not recognized in all US states — only a small minority of states currently allow couples to form one. Most states have abolished it or never permitted it. Second, no state automatically grants marriage status after a certain number of years of cohabitation alone. States that do recognize common-law marriage require mutual intent to be married and publicly holding out as a married couple, not just living together for a set period.