I used to escort many families for healthy children and SN children, before their travel, I would follow up the kids' update report.
Your doctor's explanaination in somehow are correct, but for another important reason, is that people in the countryside could offer to fix their child defects, so they choose to quit. As law regulates, it's illegal to abandon baby, so they would choose orphange and some public space for abandon, so that babies are easily to be found.
Special Needs like Down Sydrome, Spina Bifida, kind of nerve system illness would honestly be reported by orphanage, but it does exist some cases that when parents come, they found out this problem without being pre-informed, mostly because some sydrom does not show up,or because lack of staff, they don't have that detail oberservation. Once these unfixable problems are found, you could submit the decline for re-match.
As to your age problem, you'd better consult the related law or some big agency for this issue.
Helen
China Fun: this is my website for adoptive famlies and people who are interested in China to have culture share.