Yes, I agree that A is correct. The verb support is a transient verb, which means that it requires an object. In your sentence the whole that clause clause could be considered the object of "supporting".
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.
Mister MicawberSorry, but I do not find it natural at all. I see no answer there that is correct. I see that it is a mock test and not an official ETS test, so an error could well have crept in somewhere.