I don't understand. What difficulties would these Chinese companies face if they held their training overseas?

The US could impose secondary sanctions to close the loophole, or pressure these countries behind closed doors to not allow these data center uses. Since the only goal of the export restrictions is to hamper Chinese AI efforts, that would be a logical step. If there is one thing that is certain then it's that the current US administration doesn't care at all about open trade and international trade agreements.