If you'd fill your bag with batteries that's one thing but having a camera and three spare batteries to the same camera is another. They may ask you to show that the batteries fit the camera and that they work, so keep them charged, but there is no need for panic. Everything contains batteries today, even my BT headset, GPS navigator and whatnot.
Exactly. If they'd prohibit all LiIon batteries, you'd end up leaving all of your battery operated equipment off board. Not just cameras.
Anyway, it is totally different story if you send the camera as a freight. When I sent my NEX 5N for IR conversion from Finland to US, I was forced to send it w/o battery.
And if you check the packaging of a camera when it arrives e.g. via parcel service/air mail, there is disclaimer saying that the package contains LiIon battery.