Friday afternoon, he learned exactly what that meant.
After receiving his first question at his introductory news conference -- "Are your shoulders big enough to carry this franchise?" -- Barrett seemed confused by the query.
"I haven't even played a game yet," Barrett said, "so why are you going to ask me a question like that?"
Without missing a beat, his new coach, David Fizdale, responded, "Welcome to New York," drawing loud laughs from the assembled crowd.
With that, Barrett and second-round pick Ignas Brazdeikis were officially welcomed to the Big Apple.
Barrett made it clear he was still excited about the opportunity.
"It kind of feels better, to be honest," Barrett said, when asked how it felt to wake up a Knick. "I'm really happy to be here."
Both the Knicks and Barrett got their wish for a partnership Thursday night. New York turned down overtures to move down from the No. 3 pick, because they had targeted Barrett from the moment they landed there in last month's draft lottery.
Although the Knicks had the worst record in the NBA this past season and had dreams -- like every other team -- of landing Zion Williamson in the draft, they were more than happy to have the consolation prize of taking Barrett, the presumptive No. 1 pick at the start of the season.
"I think it's important for people to understand how much time we spent with RJ," Knicks president Steve Mills said. "We saw him in Chicago, had a chance to meet with his dad. ... He came and spent 2½ days with us. We took him out to dinner twice, he came to my apartment and we watched the NBA Finals together. ... We spent a lot of time getting to know each other and understanding that he had the things we were looking for, and I think we had the things he was looking for.
"We spent a lot of time getting to know each other. We knew who he was as a basketball player, but we wanted to get to know who he was as a person, and a competitor. That was important for us."
Now the focus shifts to free agency; the Knicks -- armed with a pair of max salary slots -- will be going after big names. Fans here are dreaming of stars like Kevin Durant, Kawhi Leonard and Kyrie Irving choosing next month to play at Madison Square Garden.
Mills twice batted away questions about free agency, saying it was a day to focus on the draft picks. But when asked what his message to the fans would be, Mills reiterated the need for patience.
"I think we're asking them to continue to be patient," Mills said. "We laid out a plan when [general manager] Scott [Perry] came on board and then David joined us, that we were going to build this team the right way.
"We were going to draft well and be diligent about how we build this team, and not take any shortcuts and follow a path, and we believe these two guys are part of that process. The young guys we added over the last two years, the draft picks we've acquired, and adding good, quality basketball players that compete, is important."