I wonder when exactly in "spring 2003" this was recorded in "Omar's bedroom". John was on tour in Europe with the Chili Peppers since at least January 23rd. TMV joined them on that tour on March 5th and continued touring in Europe until 9 days before the Troubadour show (April 24th), so they must have also rehearsed with Juan during that period. After Coachella they toured the states with the Chilis until NorthSix (May 21st). A few days later Jeremy died (May 25th). John started touring with the Peppers again on June 2nd in Florida (and TMV were supposed to open for them). It was said that Jeremy was the only member that returned to the west coast after the tour. All things considered there are only very few time windows when both, Omar and John, were in LA at the same time in the spring of 2003. My guess is that it was recorded in the days shortly before or after the Troubadour and Coachella shows (the Chili's played at Coachella aswell and there are photos of John hanging out with TMV on site).
Another interesting thing: John was recording "Curtains" in the days of TMV's Wiltern shows. No wonder Omar guests on the album, while John joined them onstage.