Stana didn't actually say that. She said that "when the question of more depth (ie: the serious stuff and the tough stuff) comes up, he bounces" and wondered if that would be enough for Beckett.
She also said that Beckett is the type who would want depth in her partner just as she has depth. She never criticized Castle as not having enough depth.
As their relationship progresses, each of them are going to have to deal with the tough things and cement their commitment. Castle has done well so far but he hasn't really dealt with any major "cut and run" kind of situations where he has to deal with something difficult with or about Beckett that may force him to do what he's done in the past.
Not that he's to blame for it, but he's typically ducked out when things got tough. With Demming, he didn't fight for her, he just turned and ran away from the tough stuff. There have been times where Beckett has asked him, pretty much point-blank, what he felt for her and he didn't speak up. He avoided the answers because it would have been a difficult conversation to have at those times. And when her life was in danger because she was still chasing after her mother's killers, he tried to convince her to back down by telling her that he loved her. It was a moving and fantastic moment, yet when she met him with anger instead, still stung by finding out that he had kept her from the truth about Mr. Smith for a year, someone who could give her the answers she so desperately needed all along, he gave up on her completely.
Again, WE all know that there are circumstances behind all of those things, but imagine the impression this has given Beckett without that added knowledge. Every time things get tough, Castle runs and fails to face the challenge head-on.
So yes, it's understandable that Stana would say that Beckett may be wondering if Castle is capable of dealing with those tough moments. What happens when they have their first real fight? Will he just give up and run or will he stay and work it out? She knows that Castle loves her but that hasn't always been enough to keep him around in the past, so she's bound to be wondering if it'll be enough to keep them together no matter the obstacles or tough times they may go through along the way. Will he cut and run at the first sign of trouble or will be prove that he can handle the serious stuff and the commitment necessary to be a one and done?
She definitely wasn't putting Castle down or saying he lacked depth as a character. Rather, will he be able to deal with the types of things he hasn't been able to deal with in the past? He's great when things are fun and everything is going as it should, but will he still be great when times get tough?