So, it's a case of the stupid people ruining it for the rest of us? I'm guessing you were not in a position where you ever talked to anyone who had even the slightest clue, otherwise you wouldn't be saying this. I have had to be a part of both ends, and I can tell you that I pick up very quickly whether the other person (caller or tech) is a moron or knows what they are doing. Two actually tech-savvy people can usually pick each other out, and I've had some great calls talking to someone who has a clue, but one or both of us is a bit stumped by this particular problem. And, it's a whole lot faster than if you get the usual T1 monkey with a script. If you don't have the people and/or technical skills to pick up the different types of users, then you are probably in the wrong job (sorry for the insult). As someone who really does know what I'm doing, I don't mind if the first question is "Have you tried rebooting it?", seeing as, just as you noted, sometimes we all forget something obvious. But, if I answer "Yes, have rebooted it twice, and the problem is obviously not being caused by that, as it's actually xyz", and they reply "Can you please reboot it again?", my reaction is usually not a particularly happy one (unless of course it's a "I've just made a change, can you try now?").
TL;DR: a good tech support person can tell the difference between someone who thinks they know what they are doing and one who actually does, and responds accordingly. Yes, they might cover the basics just to check, but they're not going to infuriate that person with a dumb script.
So my advice is to be polite but be clear exactly what you have done and exactly what the problems/symptoms are (being honest with yourself on your own level of knowledge, as we tech-savvy people tend to somewhat over-estimate our abilities in areas that are not our primary domain), and listen to what the tech has to say. If they say something stupid, politely make it clear why that isn't relevant. If they keep trying to push a script that clearly isn't anything to do with the problem, then ask to get escalated. Make it clear why you need to be escalated without being insulting or rude. At this point, they should go off-script to actually help, or escalate you. If they don't, repeat the "Please escalate me" (or "May I please speak to your manager") line, with increasing force until you get heard. As far as I'm concerned, if a tech can't tell that they are genuinely outdone by the caller and refuses to pass you on to someone who might actually be able to help, then the requirement to stay calm and polite fades. I wouldn't recommend outright insults and swearing at someone, but there is a point where I've had techs be stubborn enough that they are just wasting my time and theirs, and that's not acceptable behaviour for someone paid to help the customers.
But again, to temper this, don't be so arrogant as a caller that you won't listen to actual advice. Remember, you called them for help.
I love tech support calls (both receiving and making) where the person on the other end of the line picks up that they don't need to dumb-down the conversation, and can move more quickly through the steps, or completely skip ones that aren't relevant. "Can you do a traceroute to 1.2.3.4? Ok, that drops after the second step?" is so much nicer a conversation than having someone tell me "Please click on your start button, then go to Run. Now type see-emm-dee and press Enter. Have you done that?" "Yes, of course I've done that; let me guess, you want me to try pinging the gateway's IP address? I told you, I already tried that before I called you, and while I was waiting for you I just tried a traceroute. What do you mean you don't understand what I just said?"