This doesn't really explain anything at all about the recording question from what I see, it's pretty much vague and useless. Doesn't mention the HD Homerun much either, just, "XBMC with HDhomerun support for ATSC, DVB-T/C, and even USA Cable." and "your ATSC OTA device".
Same on Amiko's own site:
http://www.amiko-a3.us/?page_id=42
I'm interested in the Amiko A3 myself, but at $249, you'd think there would be a bit more info on it. I see mentions of interesting things such as XBMC and OTA, but nothing with any real substance to it. Maybe it should actually say on their site whether it can record OTA or not, you'd think something that touts itself as a Home Media Center might include details like that.
Dee Ann, probably PM Brian, [Titanium] and ask him about the OTA recording, whether it can do it or not. He's a dealer and I'm sure he'll be able to tell you and not give you grief about it.
Or, like suggested, maybe you could search better and find it yourself. Though I'm at a real loss of where other than the manufacturer's and supplier's websites might be better and more reliable to get the information from. If it says anything about recording on either site, then I sure missed it.
My guess would be that it can record through XBMC on it, but it doesn't even really actually say if XBMC can be installed on it or not. The write up on it could definitely be better.