I used to think that is how hybrids worked, but I really think in my 3rd gen Prius, the battery assist during acceleration is pretty minor (for this reason, it doesn't have a problem with draining on hills).
I believe most of the gas savings in the Prius (mine at least) comes from shutting the engine off at low and zero load, and from regenerative braking.
Anyway... to discuss the topic of the thread, my experience with a Prius is that the battery may get the most attention, but it's not as big of a deal as some may think - right now, I can buy a new Prius battery from a Toyota dealer for $1500 plus core and installation.
The 3rd gen Prius has a huge problem with head gaskets blowing and this is a fairly expensive repair. It's not clear why they have this issue. Other costly possible issues are the inverter and brake actuator - these are both hybrid-specific. But they don't seem to be as common as head gaskets in this gen.
My son's 2nd gen doesn't have the HG issues. But he had a failed evaporator core, which would have been an extremely expensive fix (we DIYed it).