Can I use basic iPhone 5/5s/5c with Aio Wireless "Aio Basic" plan?
Yes, it would appear that this is allowed, but only as long as you go the Bring-Your-Own-Device route.

In the Bring Your Own Device option of ordering the 40$/mo Aio Basic plan, you can search for Apple iPhone 5 and, subsequently, select the Nano SIM Card option (the only option available), where they will also ask you for your IMEI number.

This also has been confirmed by a service representative through the online chat function:  you cannot purchase an iPhone 5 together with the 40$/mo plan, but as long as you bring your own device, going with the 40$/mo plan is completely OK.  They also claim that the throttling past the allotment would be down to 256kbps, although this is not written anywhere on the web-site itself so far.

At 40$/mo, this plan would be more expensive and with less data that T-Mobile USA's online prepaid special 30$/mo 100 minutes + unlimited data with 5GB @ 4G plan (available only online and through Walmart), but it's still a great deal for what it is.