DVR Equipment

At the end of January we bought a Smart TV and turned in our 15 yo cable box with a DVR.  When we picked up the X1 equipment, we thought we were getting a DVR and our bill shows it includes a DVR (we put most everything on the DVR to avoid all the ads and only watch sports live).  However, what we got was a TV box and and not a DVR so that all recordings go to the internet.  Today we were told that we could not get a DVR to physically hold our recordings, that Xfinity recordings all go to the internet.  What is happening is whenever the internet is down (we have had at least 5-6 interruptions within the month) we cannot access our recordings which was never the case with the old box and the system locks up our TV.  Is it true that all X1 recordings go to the internet? Are there no DVRs available to keep our recordings?  Is our only option to go to TiVo?   Secondly we were told that only 20 hours of service is covered by the X1 package and weare paying for approximately 150 at $25 a month.  If these things are true, then X1 is a reduction in service, not an improvement.  I would like to have some confirmation of the DVR status and recordings.