“This was something we had an indication was likely to occur,” Mr. Earnest said. “But it’s not something we requested.”
So the Brits call up, say "hey, this chump's partner is coming through Heathrow, you want us to detain him?"
That's all the Brits needed to hear - nothing, no objection to the planned detention.
Obama consented to, approved of, and ratified this detention, notwithstanding that he, or whomever answered the phone, didn't actually say "yes."