Putin's telling the truth, actually. The USA has no official residency list for localities, so people move around and die and etc. and nobody finds out, and they can still vote. They also often don't test eligibility for voting, they just send everyone they can think of a voting slip. Total voting slip spam. They end up all over the sidewalk.
And you don't even have to return the slip, yourself or make any effort at all. Maybe you're not voting because you don't want to vote, or don't know what is going on. Activists go to people's houses, door-to-door, drug treatment centers, old folks homes and hospitals, and "help" them fill out slips, often in exchange for presents or money, and even if that person is senile or afford or barely-conscious, and then collect them all in a big bag and mail them off.
Other places have mail-in voting, but nothing like that. Whole thing is bonkers.