I don't see where it says that. Unless those are the game statistics that are replacing the target's. If you're just adding new speeds, saving throws, skills, vulnerabilities, resistances, immunities, senses, languages, special traits, actions, reactions, and limited usage abilities that the target doesn't have to their game statistics, those game statistics aren't being replaced. They're being added to. You can't have your cake and eat it, too.
I'll admit I have to start by playing the common sense card here, if I use a lvl 9 spell to take the form of a bird; I better be able to fly. If I turn into a big bad dragon, I better have a claw and bite attack, saying they can't do that removes the entire point of shape changing. After all: the spell says you take the form of a creature who's CR is 20 or less, a CR 17 adult gold dragon is Huge sized, can fly, has a breath attack (2 options even), can change shape and breathe underwater. Taking any of those away undeniably lowers the creatures CR. I'd also like to point out that the new DM errata (http://media.wizards.com/2015/downloads/dnd/MM_Errata.pdf) specifically mentions under the 'legendary creatures' section (and I quote):
“If a creature
assumes the form of a legendary creature, such as through a
spell, it doesn’t gain that form’s legendary actions, lair actions,
or regional effects.”
There is no other limitation placed regarding this on shapeshifting and abilities in any of the books or errata's, this would strongly imply that ALL other abilities do become available.
It would be replacing because you'd be removing the old factors mentioned (ability scores for example, new scores might be lower then your old ones, they don't add together, they get replaced.) Monsters rarely have skills though in the cases that they'd do I'd say they'd replace the old ones, regardless of if the original scores were higher or lower. The part where the PhB says that actions such as casting spells might be limited in this new form also implies they still know their spells, meaning they retain all knowledge from their previous form (meaning spells, class abilities etc are all fair game).
I could imagine a DM confronting their players and tell them this play is too strong and he doesn't want to use it, which is completely fair and his or her right as a DM, but judging exclusively on the rules in the book, I'd say it's very much possible.
An interesting idea could be that the DM decides the players have to spend a significant amount of time in their new form before they become able to do certain things, effectively 'creating' imaginary lvls over 20 in order to get their unique abilities like flying and a breath attack; it'd make sense you'd have to get used to a new form before you can use it effectively in my opinion. (looking at you captain ginyu, cheating in db super >.>)