I bought my AT&T Aria about 3 weeks ago, my very first experience into the world of smart phones. It is Not True! When you buy the AT&T Aria with the AT&T version of Android 2.1, with all those useless AT&T apps, you ABSOLUTELY CAN download apps from the Android Market Place! There is an extra tab in the Market Place that says "AT&T Market". You are NOT restricted to ONLY AT&T Market, or AT&T apps!
Why this becomes a problem is because the internal memory of the Aria is limited compared to other smart phones. Only 500 meg or so. With the AT&T version of Android 2.1 with all of their pre installed apps, there is only about 108 Meg available for you, the user to download apps from the Android Market.
It is this situation that led me to learn about rooting, and ROM flashing. If you go down this path, be advised that you are voiding your phone's warranty with AT&T.
First, learn how to root your phone. Then, install one of the Android 2.2 apps. Once you reboot your phone, you can start to download any apps that you want, (even non-market apps which need to be side loaded). You will be able to njoy the full potential of your phone, which includes installing your downloaded apps on your SD card, something AT&T stock 2.1, (or any version of 2.1 for that matter), doesn't permit.
My experience is that once the Aria is rooted and most apps are defaulted to the SD card, the phone is very fast, with fantastic features. It packs a LOT of power into a small package!
Hope this helps!