Yes.
I really don't know what specifically the High Commissioner testified to. Their monitoring report was simply a report as to whether the terms of the agreement, namely, the implementation of the exceptions, was being fairly done, and they concluded that it was.
The UN High Commissioner for Refugees is under very real constraints as to their ability to criticize the U.S., especially in a very public forum like this. They have specifically found that detention of asylum seekers violates the 1951 convention.