I logged a support issue with Yamaha for this issue over a year ago when I first "upgraded" my receiver from the 1065. I ended up purchasing a $100 Insignia to be able to get FM reception. Finally in August I was fed up with this work-around, so I started bugging them about a fix. Apparently the Axxxx series used the same chip and had similar issues, so Yamaha was forced to come up with a fix for those receivers & the support manager indicated that he was going to push to get the fix for the 1065 & 2065. The support manager was quite responsive once I was able to get in touch with him, and even gave me updates every few weeks for the status of the firmware fix.
I received a call on Thursday indicating that I could download the fix from their FTP site. I just had a chance to try it out and stations that were completely unlistenable are now listenable. There is one weak station that the Insignia pulls in with a lot of noise that the 2065 sporadically locks and unlocks, but for the listenable stations the firmware fix seems to have worked.
I don't know if the update is available generally yet, the version is V037_104_038, so you want to watch for that version or later.
So almost a year later, I finally have decent FM radio in my 2065. I will need to retry AM at some point, but I am not as interested in that.
If the network update doesn't provide that version, try again in a few days. I suspect that once they get enough feedback that it is working it will be generally released.
It was a long wait, I am glad that they could fix it with a firmware update (note that it updates the DSP firmware).