In Barbie's case, yes, you're mostly right.
Reasonably well fitted plates worn over fatty parts of the body don't need padding. For example, I don't need padding over my beer gut if I have a properly sized and fitted plate there - you could hit me with a 16lb sledgehammer and you'd just knock me over. But if you hit me on an unpadded plate over the ribs, the lack of "natural padding" would allow the shock to transfer and crack or split my ribcage or its connecting cartilage.
In SCA combats, I've seen very fat men wearing plate with little or no padding taking blows that would have sent me to the hospital. But the only place Barbie has any "natural padding" is her breasts and buttocks... and only the latter is practical to leave unpadded, because the shape of her bust would be near impossible to fit (the edges of breast cups will tend to be driven into the chest armor, and she's got zero fat everywhere else on her torso so she can't just use an unpadded single plate cuirass). The rear tassets she's wearing over her butt are the only place it would be both reasonable and practical for her to skip padding.
So yes, in Barbie's case she needs some kind of padded jack, gambeson or hauberk under her armor. Preferably an eyleted gambeson with strips of mail sewn on beneath the gaps in her plates (which are necessary in order to get the plate on the doll, of course).
The armor shown also needs a mail aventail and skirt, but it's actually a pretty damn good start. Kudos to the designers.