Me, too. When I first read it, I literally crapped my pants.
Claming that “literally” is descriptively clear just because famous authors used them is Argument from Authority. Not using the phrase “literally” figuratively makes for clearer communication no matter who uses it. Used properly, it can also be a device to communicate humor, but rarely used that way in its figurative sense.
Now I am not faulting people for not prioritizing clean communications: I sometimes use “physically” figuratively, but rarely twice in the same conversation, since I catch myself. The overhead required to monitor everything you say would be less than the communication clarity lost by occasionally slipping up. But three times in a short conversation is hardly a minor slipup, but forgivable since “literally” no longer means “literally.” i.e. if you said “You literally have to click on the web link”, the recipient might still have a lingering doubt as to whether the process could be automated or not.
I don’t think that’s the point. I think the point is that while literally-as-an-intensifier may not be the clearest use of the word, those that do make use of it aren’t necessarily “functional illiterates”.
And it’s my opinion that clarity/unambiguity is not necessarily the only criterion by which the usefulness of a word should be judged. But that’s just my opinion.
I’m still wondering how someone could get it wrong with no adverb in that sentence. “You have to click on the web link.” Seems obvious that I have to click on the weblink. I could see using “actually” if you were trying to be a passive-aggressive halfway smartass, but other than that I’d let the verb go unmodified.
I fail to see how citing famous authors and a long history of usage is argument from authority, while citing part of a dictionary definition is not the same thing.
This isn’t physics, it’s linguistics. Usage is what defines a word.
Is using “literally” in a figurative sense optimal in any given situation? Probably not. Is it normal? Yes. Is it wrong? No. Why? Because people have been doing it for hundreds of years.
Quantitatively is a much better word
I resist the general urge toward a literal hijack! This started with a rant on “physically,” and I will defend attempts to drag the thread off topic. (Even though I didn’t start it. Whatever.)
For my part, the objection to “physically” in its usual misapplied context has nothing to do with rightness or wrongness. I ask the simple question: Does it add anything? Does removing the word from the sorts of sentences in which it is typically used alter the meaning of the statements in any material way? Or is it there solely to add to the number of syllables coming out of a given speaker’s mouth (or the word count in the user’s email) in order to puff up said individual’s importance? If the latter, I will call the individual on it, as I did above, and I won’t apologize. I am an advocate of simplicity and clarity, and I have declared pointless inflations like this to be a mortal enemy. Well, not mortal. I won’t stab you if you overuse “physically” in inappropriate contexts. But I reserve the right to think of you as a ninny. 
I spent a lot of time on the phones, and I used to use empty syllables quite a bit. It gives the other person a chance to digest the meaningful word you’ve just given him before you throw another at him.
People have been misusing the word for years, true.
In the example you cite, there’s no need for an adverb at all. Try: “We need to change the way we think.”
The poor silly woman quoted in the OP was also using a superflous modifier. Simply take the word “physically” out of all the quoted sentences and they’re fine. Then have the woman spayed.
If you weren’t literally beyond my reach, I would HURT you for that. 
Would you hurt him physically?
If I could actually? Really? Maybe just metaphorically.
I ask the simple question: is casual conversation designed to be proofread?
Am I disagreeing with you on this? No. Except that is it my opinion than in many situations nonoptimal usage should be avoided. When you’re hanging around your friends is one thing, but you have every right to be offended that people are wasting your time at the job or on a support line with superfluous and distracting language.
Proofread? No. Mocked, though? Sure! 
Yeah, everyone knows the proper phrase is “he blowed up good!”.
That’s the beauty of it!
Oh Gawd…
Close to this…I use the word ‘manually’ in my job where you have to use Excel or some spreadsheet to ‘manually’ do something rather than write some code and executing it.
Am I going to hell?
I don’t think physically, literally, or figuratively is the right term for the actions described in the OP. Actually or actively are better, but IMO the better term is MANUALLY.
It means a thinking body needs to be at the computer reading the screen and controlling the mouse.
I searched for the word “manually” in the thread before I posted, but I typoed in “manuallly”. So I didn’t see you beat me to it – I agree with your term.
But see how easy it is to screw up when you do things mannuallly?