That is strictly not true, I believe. In the US, some form of ID (not necessary a Photo ID) is required to vote [1]
[1] https://en.wikipedia.org/wiki/Voter_ID_laws_in_the_United_St...
For example:
Maine: No ID needed at polling place if registered to vote at least one day prior to election. However an ID is required to vote if person was registered to vote on the day of the election
Massachusetts: Non-photographic ID is accepted at polling stations.
Minnesota: Non-photographic ID is accepted at polling stations.
Some of those states are also getting legislation requiring ID for voting.