My daughter heard that from a couple of coaches. One told her flat out that she wasn't fast enough for their championships so although they would love to have her on the team, they couldn't offer her a scholarship. I think they meant it - and another, an ivy coach she had talked to early on, contacted her late in the game to ask how she was doing. When she said she was still undecided, he basically said, well my slots are used up, but if you apply and get in, we will be thrilled! Again, I think he meant it - why else would he contact her?
I would hope most coaches are honest when they say that. Also, it depends on the sport and the team. Some teams can hold unlimited team members and others (like basketball for example) are a lot more limited.
I guess how you respond depends on how likely you are to get in without support, and whether you're willing to risk being denied playing time. Also how many offers you have from coaches who really want you. Some people prefer to be big fish in smaller ponds.
Edit: I do want to add that the two coaches who said that to her were off her list before she finished reading their emails! ;-)