The symptom is caused by the Time Capsule USB port not supporting bi-directional communication. This is documented by Apple in this article. So it is not the MX320 but the design of the Time Capsule. And based on this information I would say that the HP would have the same issue, if it was also connected to the USB port.
Note that if you had a All In One that supported wireless, then it could connect to the Time Capsule via wireless and you would be able to print.
Thanks for confirming that the situation remains as it was 2 years ago: printing can be shared with the MX320 connected by USB to the Time Capsule, but scanning must be done with the MX320 connected directly (by USB) to my Mac Pro. An inelegant approach to modern technology, but doable.
The Time Capsule USB port does support limited bidirectional communication, in that it alerts when the printer is out of paper, or has some other problem. I suggest you modify your response as it caused a lot of head-scratching on my part as I was trying to figure out the logic of the situation.
My next printer/scanner will be wireless to get around this mess.