You mean as far as screenshots and stuff go? Well for starters, going off the CoD tech demo alone you immediately see that models are lower poly and texture resolution is low res compared to in game models from various games on other engines.
I'm gonna need some comparisons for that. Specifics, please.
They're not necessarily lying, though. Reworking code significantly enough can make huge changes to how it runs. Sure, you might still have certain methods called for certain things and the basic structure be the same, but that doesn't mean it's the same engine.
Even though I don't care what engine or whatever they're doing with Ghosts, I wanted to say this.
If you make changes to an engine, that doesn't make it a new engine. It's like handing down an old pair of shoes to my nephew (he won't be able to fit them in years anyway) but before giving it to him I change the laces and wash the shoes. Any way you look at it, they are still the same pair of shoes.
I'm not big on the whole CoD thing, I just play the games so it doesn't bother me as much as it would a core fan of the series. If you get what I'm saying.

Code really isn't like a pair of shoes, though.
And I think there's a bit of misunderstanding stemming from the term "engine". It's not like a car engine, where there are specific parts that must be there and where some parts are objectively better than others. It's code. You can modify code to such an extent that it performs so drastically differently that, though it may have been based on code used by the previous "engine", it behaves in very different ways than the previous engine.