Rhone would be correct to believe that Urban had asked out of more than just mere curiosity - but when Rhone stepped in to speak, when the Enchanter opened her mouth to comment, he took a step back - closing his own mouth. He wasn't here to dominate the contact's time, nor stifle the questions or observations of his allies. He had brought them not because he wanted them to quietly obey his orders - but because he knew he couldn't do this alone. Each of them had their own talents, and sometimes a Lieutenant's best option was to just get out of the way.
A nod was given to Elise as she mentioned setting up a meeting with the Templar who had been at the meeting. The answer with the Wardens ... it was acceptable. The question's point was to provide more of Elise's intentions, rather than to take any advice from her on how to handle the Wardens. If she had wanted to stick her nose in, to become a crusader for all fronts, well her intentions of changing up the leadership of the Chantry for her own game might've been more clear. Or she might've been a simple, overly ambitious sort. All Templars were affected by their Lyrium to some degree - and in meeting a new one, especially one who spouted controversial ideas that the Chantry might not be as just as it is meant to be, it was important to make sure it wasn't just the Lyrium talking. Elise seemed pretty competent and collected, which added weight to her words.
"They'll not have you," he added, his gaze shifting over to the Enchanter Eileen. "I'd like to meet with this contact - as quickly as possible." Their investigation was one thing, but he wouldn't risk one of Ferelden Circle's last mages to a political power struggle.