Edit: You are correct, it seems the PS3 does have a built-in PSU that can handle 100-240V without an external transformer, although I'm not 100% sure this is the case for all PS3 models.
The voltage range is printed on the inside of the PS3 unfortunately as far as I know, so I don't think you can check without taking it apart. I didn't find any info online to suggest that there is a PS3 model that uses a 120V only adapter, but you may want to consider contacting Sony support for absolute confirmation.
This would most likely be caused by having a step-down transformer that is not equipped to handle the high amounts of electrical current being drawn from the PS3 while it is under a heavy load (i.e. during gameplay).
The PlayStation 3 (especially older 'FAT' models) can use more than 200 Watts of power at any given moment. Compared to most electronics, this is a lot of power, and most step-down transformers are not equipped to handle so many Watts (many transformers are limited to say 50 or 100 Watts).
You may need to purchase a new transformer, preferably one with a 250 Watt or higher power rating (a 200 Watt or higher rating would be satisfactory for newer 'SLIM' models).