It shouldn't really be that hard to believe.  The Wii is an abberation.  The N64 was more powerful than the PS1 and the Gamecube more powerful than the PS2.  Furthermore, Sony took a pretty big financial hit by releasing an incredibly powerful console this generation, so they may want to scale things back.

For PS4 only VRAM of 1GB is rumored (because the HD 6670 typically uses 1GB), but of course also the GPU and CPU in the APU need Ram. I'd be surprised if PS4 or Xbox 720 have less than 3GB of total Ram.

And regarding the heat and price of cards:
HD 6770                               :   Furmark:  ~100W   Price: ~80€
HD 6670 (GDDR5-version):   Furmark:  ~ 75W    Price: ~55€
HD 6550D                            :   Furmark:  ~ 55W*  Price: ~35€/50€**

*only GPU-part power consumption; but I couldn't really find good reviews which only measured GPU-power usage in furmark so this value is an educated guess based on a high number of different tests and reviews; might be off by 10-15W

**The A8-3870 costs around 95€, but also the CPU-Part is included in that price! Similar performing AMD-CPUs without a GPU cost ~75€ so you only have to pay an additional 20€. But as the GPU in the APU needs additional Ram you will have to pay around 15$/€ for that (if you want 1GB of GDDR5). So all in all you have to pay around 35€ for the GPU in the APU.
Similar performing Intel-CPUs cost ~60€ so if you use that you get a total cost of 50€ for the additional GPU-performance (but I have no idea if Sony likes Intel and using Intel-CPUs is even an option for them).

I used prices as they are in Germany as of today. To get US-prices in dollars you will have to multiply the numbers by 1.1-1.2 .

In my opinion there's at least no problem with the price. PS4 will probably be priced higher at release than the Wii U will be and the additional cost of around 20€ for the GPUs will be no problem. But I still doubt that Sony is using such a configuration (both GPUs are a little too weak imho; perhaps they are using a really customized design of both and hence the real numbers will be totally different).

The APU of AMD can drain a lot of power, but that is primarily because of the CPU part. But as the CPU part in most cases can be undervolted quite a bit this can lead to much less power consumption if you pick the right dies. Still heat may be a problem (but the cell-CPU in the PS3 also had a high TDP)