It was about 15 years ago, before HTTPS, that suddenly my browser couldn’t find anything. I happened to know a couple of actual IP addresses (including the Unix server sitting in my office) and had no problem getting through to them. So I called my ISP (Bell Canada, as it happened) and spoke to their “help” tech and told him that their name server wasn’t working. First he asked me what a name server was. Their “technician”, this was. So I explained to him what it was and what the problem was. He replied that there was no problem at their end and maybe my IE was defective. Oddly, my IE worked fine the next morning. I soon got another ISP.
Back then, probably a lot of servers were not host-header configured.
But yeah, 15 years ago is a little late to not know about name servers (or that this meant DNS server). I had dial-up in the early 90’s and high-speed by 1999. The internet was pretty well established. Most likely you were talking to front-end script jockeys, the unenlightened ones who went through a list of fixes for typical problems… (“Have you tried rebooting?”)
Yeah, it’s not uncommon for sites to actually share an IP address these days, and differentiate them based on the URL used to access them. And HTTPS certificates are usually for the canonical name, not the IP address.
One thing you could try is adding the IP address and host name to your hosts file, which would allow you to bypass the DNS server and just go to that IP. That way you’d actually request the proper URL and not just an IP. The file is located at C:\Windows\System32\Drivers\etc\hosts on Windows, and includes an example to show you the format.
I’ve never tested this for either purpose, though.
I note you can also just change DNS servers and see if any of them already have the record, or are still behind and have the old record.
I’ve done it hundreds of times. If you know the IP, it works like a charm.
… And if not present, the host header is inferred from the request. Because HTTP 1.1 required a host header, but HTTP 1.0 did not.
So
GET hostname
will probably get you something:
GET 191.168.1.1
probably won’t.
Some years ago, long before anybody heard of https, a small text-MUD I played on could not be resolved by Cox’s DNS for about two weeks. I pinged the server from work and used the IP until the DNS got an update or something and it worked again.
Maybe belaboring the obvious but you need DNS for this to work… 
Just saying! 
Of course your advice is true (and I use ping all the time for this).
One reason to not use the IP address for anything other than temporary access is that it typically changes, and you will have no warning. My own web site has used at least 6 IP numbers over the last 25 years; some because I changed the host, and some because the host altered their system internally.