This explanation makes no sense to me...
Like I said, I have been checking for software updates regularly - since about 3 days before Verizon announced the OTA (and then later, said "jk").
There is absolutely NO WAY that the servers were "overloaded" then, and still are! Nearly every day between then and now, I have checked for updates, and I get the same error\message.
Either this is a false explanation - or Verizon seriously needs to put some money towards upgrading their servers.