Josh Jackson said all the right things about potentially playing for the Celtics on Wednesday during his media availability session in New York. He refused several offers to come to Boston to work out for the team, yet he maintains he has no issue with playing for the Celtics.

Meanwhile, Jayson Tatum came to Boston last Saturday, worked out in Waltham, met the coaching staff and, of course, ultra-prepared coach Brad Stevens laid out plans for Tatum should the Celtics select him third overall on Thursday night.

It seems like the right fit, a more natural fit. And unless Stevens and president of basketball operations Danny Ainge want to outsmart themselves, Tatum should be their pick, and they should move forward with another potential cornerstone.

Tatum has the offensive polish the Celtics could desperately use because defense, as important as it has become under Stevens, is not going to win championships in the era of the current Golden State Warriors. The Cavaliers shredded the Celtics’ defense in the Eastern Conference finals, and in turn the Warriors shredded the Cavaliers in the NBA Finals.

Defenses are not going to hold these high-powered offenses to 90 points, so the Celtics need players who can score, who can execute the pick-and-roll with Isaiah Thomas, and who can consistently hit open jumpers. Tatum, who is listed at 6 feet 8 inches and 204 pounds, shot 50.4 percent from 2-point range and 34.2 percent from 3-point range in his lone season at Duke.

Tatum is offensively skilled and can learn defense in Stevens’s system. And most important, he has the ability to play power forward. One thing that Stevens told Tatum is that he is capable of guarding four positions on defense, which would help the Celtics greatly.

“I talked about that with coach Brad Stevens,’’ Tatum said. “He just said guys that are my size and are versatile offensively and defensively, it’s hard not to play those guys. That’s what we talked about. If you can defend 1 through 4, if you can knock down shots, and then if you can score, that’s a bonus.’’

The Celtics obviously have scouted these prospects extensively and felt that one or more was at least as good or a better fit than Washington’s Markelle Fultz. That’s why the Celtics traded down with the 76ers to get the third pick and a future first-rounder.

Jackson is raw offensively and needs to work on his release. He is a maniac defensively and brings plenty of energy. But what does it say about a player when he won’t work out for a team that until Sunday had the No. 1 overall pick?

The Celtics still weren’t able to get Jackson into a gym for a personal workout. And he has been left to defend his character after an off-the-court issue in which he damaged a female student’s car after a dispute at a party. He was charged with misdemeanor property damage, and he also was suspended for Kansas’s Big 12 tournament opener (a loss to TCU) for getting into a minor car accident without informing his coaches or the school.

Those could be considered minor issues, but with these athletes being such an investment for teams and the lure of the NBA life awaiting, they are red flags. The Celtics shouldn’t pass up Jackson because of those issues, but the fact he refused to work out for them doesn’t help his case or character.

“A lot of the character issues that you guys probably have been reading, they’ve really been blown out of proportion a lot,’’ Jackson said Wednesday. “Obviously, I did a few things wrong that I shouldn’t have done, but it’s been blown up a lot. It’s because I am who I am. People who were close to the situation, the teams that are considering drafting me, they know exactly what’s going on. They know exactly what’s happening.’’

Jackson said the right things, such as he would “love to play in Boston,’’ but this should be the case where the organization takes a long look at how each player has conducted himself during the process, compare the talent, and then decide on Tatum.

It’s not an easy decision. Jackson could potentially become a cornerstone for a team, and the Phoenix Suns, who have the fourth overall pick, would certainly be happy to get Jackson. But if Tatum is a better offensive player, delighted the team in his personal workout, has the upside to become the team’s next great power forward, then why pass?

Ainge said he isn’t afraid to draft a player who hasn’t worked out for the club. But it is a risk. You want players who want to be Celtics. Prospects shouldn’t have to be talked into playing in Boston, a team with 17 championships and coming off a 53-win season.

So the choice after careful deliberation should be obvious. The Celtics already have taken a serious risk by passing on the opportunity to take Fultz to acquire a future first-round pick, but play it smart and sensible, bring Tatum into the program, and then concentrate on free agency with another talented prospect on the roster.

Gary Washburn can be reached at gwashburn@globe.com. Follow him on Twitter @GwashburnGlobe.