Absolutely bothers me. Absolutely should investigate. And absolutely should retract statement if he (Trump) is just bullshitting people.
Side bar:
That is why I always wanted something like this.... [every single person that lives legally in this country to be issued a voter ID card, something like India does for its 1.x billion people. Now before any of you guys scream racist and voter suppression and all that jazz. The ID card would be free to all USA people; and given out at your local DMV, or city hall, provided you were able to prove you were a citizen. (use your SS card, state issued ID card, passport, whatever the DMV allows). Renew it online or at the DMV for free every so often.]. It's just an IDEA, so please don't go all Jim Crow on me; that is not what I would ever want.