Right call here, as that broad the statement is not correct.
ยง4b BDSG, Absatz 2. See https://www.gesetze-im-internet.de/bdsg_1990/__4b.html. The gist is: You can transfer data if you inform and the data protection is adequate. Then Safe Harbor collapsed, that was not the case anymore (also before, protection was not really adequate, but that was partly ignored). Thus Privacy Shield to give a new legal foundation. If now that collapsed as well, transferring personal data to the US will indeed be illegal again.
ยง4b BDSG, Absatz 2. See https://www.gesetze-im-internet.de/bdsg_1990/__4b.html. The gist is: You can transfer data if you inform and the data protection is adequate. Then Safe Harbor collapsed, that was not the case anymore (also before, protection was not really adequate, but that was partly ignored). Thus Privacy Shield to give a new legal foundation. If now that collapsed as well, transferring personal data to the US will indeed be illegal again.