so i feel secure in claiming that i am more a walrus than a fish and therefore qualified to opine about water
i do agree that identity and hidden mutability are important aspects of the oo view of the world, and that the author of these slides is off-base about what oo is. but i think that the essence of oo is that computation is done by sending messages to objects, but sending the same message to different objects invokes different code. this feature is present without mutability in bicicleta, and in abadi and cardelli's untyped ς-calculus, which it's based on; the ς-calculus was invented to formalize the essence of object-oriented typing
the original intuition behind oo was to decompose a computer system into smaller computer systems, like a computer network; each object in the system was in effect a tiny computer, with its own private code and state. this was inspired by alan kay's undergraduate degree in biology, which mostly studies organisms made out of cells, which are basically tiny organisms. and in that formulation, obviously hidden mutability is the default, because you can't prevent a computer from changing its internal state as a result of a packet you send it; and mutability generally means identity is important
but even more central to this formulation is the idea that different objects can behave differently in the same circumstances
obviously none of this has anything to do with memory layout! except very indirectly