Hi Suzette,
Many third-party manufacturers will not tell you that the cables they manufacture will not work with newer Apple products. All of the official Apple A/V cables for their newer products contain a chip which must be present for the video and/or audio to play correctly. Apple does not manufacture an HDMI adapter for any device except the iPhone 4S and iPad2 at this point (
Apple Digital AV Adapter - Apple Store (U.S.)), so any third party product is not going to work, or will work with limited functionality. It seems greedy of Apple to do this, but it is their way of providing products that "just work" as they are supposed to. When third parties attempt to circumvent Apple's tech specs for a device, this is when the problems happen. Unfortunately, if you don't have an iPhone 4S or iPad2, Apple is correct in telling you the only way to connect your iPhone to a TV is through AppleTV. Or, if your TV has the "quickly-becoming-antiquated" composite or component connections, you can use the AV Digital cable that you mentioned.