To play devil's advocate here... I spent about 6 months working in a call center and a lot of them are very compartmentalized. It could be very likely that the people you are talking to cannot see nor know anything about the website, why something isn't there, etc... Most are just like us. They get up, go to work, and go home. So if they seem to be unaware chances are, they are completely in the dark.
That said... they should be able to log a trouble ticket somewhere with a higher tier tech support and try to figure out why it's down. Heck, if you call into a lot of OEMs (looking at you Ford) customer service can't even talk about warranty tickets with you because it's a completely separate system that they don't even have access to. They have to submit a request to the warranty department and wait for the information to come back and then send it to you.
Your post reminds me of a situation I was in the midst of in 2002. I was working in one of Houston's premier Ford dealers, on a then new design Explorer. I was an automatic transmission specialist at that time, which required a very deep knowledge of electronics, due to the nature of the EEC controlled transmissions, and the need to be able to diagnose drivability concerns due to those causing or contributing to auto trans proper functions.
We had a woman who'd bought a new design Explorer that summer. In August of 2002, she had put about 3-4 thousand miles on it. She brought it in due to intermittent cooling of the A/C temps out of the passenger compartment vents.
I got involved because of my electrical/ electronics background, AFTER it was brought back for it's 3rd time in short order for the same problem, and, the HVAC specialist was away tending to his critically ill wife.
The Factory diagnostics flow chart screamed "Bad Ecm". One thing I noticed was a stand-alone DTC of the "U" variety in the instrment cluster. (Ford calls this the "HEC" module... Hybrid electronic cluster).
I noticed in the dealer history that 3 ECM's had been replaced.
Anyhoo, the net problem was that the ECM would intermittently stop commanding relay pick for A/C compressor turn on.
Being one of the yahoos in the big corporate structure, I followed protocol and called Ford's Tech line. That fella agreed that the ECM was a likely cause. When I mentioned the phantom/ intermittent "U" code, it didn't phase him, and he said he really couldn't see how THAT would have anything to do with the problem.
Keep in mind, this vehicle's inter module communication system was Ford's "early" CAN/BUS, named "SCP, or Standard Corporate Protocol". FEW knew anything about this new fangled way of computers talking to one another, yet, it had been in place in manufacturing for a long time.
I was directed to replace the ECM, for the 4th time. (The whole " crazy" thing about doing the same thing repeatedly expecting different results!)
So, back to your point, I was directed by the Ford Call Center to call a different phone number... to the ECM's engineering/ manufacturing guys. THAT guy, was in the process of getting ANOTHER PCM authorized for this issue. Meanwhile, The woman who owned the car contacted a Lemon Law attorney, and Ford reacted by sending a field engineer down to get involved. This put a quietus on the fixing of this vehicle and this took it out of my hands
Of note, my GM training germane to CAN/BUS systems had me taught that solving ANY DTC in ANY module was/ is required FIRST, due to the whole "snipe hunt" thing. When I tried to mention this to that engineer, he was snide and condescending to me.
He and 2 other techs in the shop had wiring harnesses and half the car disassembled, to no avail.
Eventually, the HEC module was replaced and the car was fixed. Go figure.