Supporting those who aren't even customers
Some of the hardest tech support calls to handle were those which didn't necessarily have anything to do with technology. These were calls from people who either weren't a valid contact for an account or couldn't prove that they were. This created a certain quandary because on the one hand, neither you nor a valid contact would want the site to be down, but on the other, you can't reveal any information about a customer to some random voice on the phone.
This happened to me once or twice. Somehow, a call from the outside world found its way to my phone and I had to deal with it. We had a web hosting customer who ran one or more web sites, and they in turn had customers who bought services from them. Some of those "second order customers" knew where their sites were actually physically hosted, and would try to call us when they couldn't reach their usual contact.
I tended to approach these calls from a perspective of only confirming those things which could be established by anyone on the outside world. Things like traceroute or a simple "whois" against the web server's IP address would show that it is in fact hosted with the company, so that's not a secret. However, anything pertaining to the customer, like their actual company name, or any contacts, or really, anything at all involving their account was off-limits.
Likewise, a web site which seemed unresponsive from the outside world was also no secret. I could quickly ssh home and try a connection from an unrelated IP address to ensure it seemed down to everyone and wasn't artificially working from an internal/company address (since those tended to have special routes and/or firewall entries).
The conversation would be a little stilted, but I could say that yes, I see that this site exists, and it's pointed to an IP address that is in this company's space, and yes, I also can't get it to load. I can't tell you anything about it, but I will take a look on behalf of our customer and will make sure they know about it.
Then I'd thank them for bringing it to my attention and make sure they were happy with what I had said, and then I'd let them go. Most people tended to get this: they knew they didn't have any formal business relationship with us, but they needed to do something.
I'm on the other side of the phone these days, but these things still happen. I get mail for some deli on the east coast which apparently has a very similar e-mail address. They're apparently getting hooked up with some kind of capital infusion -- good for them! Trouble is, mailing me won't help them fill out their forms. I rang up the sender, explained that I'm not a customer, but I had something for their actual customer, and clued them in. Five minutes later, everyone was on the right track again.
More recently, I came home to discover an Amazon package waiting for me. I knew I didn't have anything pending, so it must be a present! Awesome! Then I looked at the label: it was for someone else. It was the right house number, but the wrong street entirely. I know these guys tend to optimize in terms of numbers and batches and don't always look at the street names after they're loaded on their carts, so it's easy enough to figure out. Look at your boxes sometime: you'll probably see your house number written on the side in black Sharpie.
I just rang up the delivery service and filled them in, and they sent their guy back around to get things on their way. Ideally, the actual recipient won't be bothered by this at all, and hopefully the delivery guy won't get in trouble for making an honest mistake.
I've even had to do this for Internet connection issues. Back in my school district sysadmin gig days, we had a T1 circuit run from our district office, across town, and into a local university. There, we terminated it into a little router of ours that we got to park on their Ethernet. They provided an IP address and a default gateway, and also had their providers advertise a route for us. Life was mostly good.
Still, now and then, they'd "lose" us, possibly because we weren't on some list of whatever networks were supposed to be at that facility. Late one night (or was it really early one morning?), I wound up on the phone with a network engineer from their ISP, since I went to them, hat in hand, asking for help. I told them straight out that I wasn't their customer, just one level removed, but they were ultimately responsible for advertising our routes, and we were offline, so... help?
He wound up digging in and figuring things out for us, and got us back online. I had a nice chat with that guy, and he basically offered me a job. In retrospect, I probably should have taken it, even though it would have meant moving. They obviously would have appreciated what I was doing.