Don't care for CoD, so it doesn't affect me personally, but I find this incredibly hard to believe. The engine they use is ancient, and their games haven't been visually impressive for ages. I can't imagine it would be very difficult to get this running at 1080p. Especially when there are other games that look infinitely more demanding already confirmed to be running at higher resolutions. Besides, I'm pretty sure Activision confirmed 1080p for both systems months ago.
Source is also pretty laughable. Some random nobody said he played it and claimed it was 720p. Sorry but this seems like fishing at it's finest by NeoGaf to me. I call BS