The post recommends teasing. That is better than panic (ymmv), but my guess would be that even better would be a perfectly calm and deadpanned: "No." Or a longer sentence, but just as declarative: "I am not cheating on you." No details or explanations or protestations.
The problem with this approach is that factual statements can be argued with, putting you back into the same place as before -- i.e., having an argument where you're being accused of something. The "agree and amplify" approach has the tactical advantage that it leaves the other person with no place to escalate to, and can be repeated more or less indefinitely.
(Note: I'm not commenting here on the (un)desirability of having an adversarial relationship like that to begin with, just pointing to a tactical advantage of the proposed "agree and amplify" over a flat assertion or denial. Another advantage, btw, is that it can actually make the accuser paradoxically feel listened to/accepted/validated in a way that disagreement does not. My wife has actually successfully used this tactic on me when I've been annoyed at some minor thing - the old, "yes, I did do that, and I did it just to annoy you" routine. ;-) )
Followup to: Do you have High-Functioning Asperger's Syndrome?
LW reader Madbadger uses the metaphor of a GPU and a CPU in a desktop system to think about people with Asperger's Syndrome: general intelligence is like a CPU, being universal but only mediocre at any particular task, whereas the "social coprocessor" brainware in a Neurotypical brain is like a GPU: highly specialized but great at what it does. Neurotypical people are like computers with measly Pentium IV processors, but expensive Radeon HD 4890 GPUs. A High-functioning AS person is an Intel Core i7 Extreme Edition - with on-board graphics!
This analogy also covers the spectrum view of social/empathic abilities, you can think about having a weaker social coprocessor than average if you have some of the tendencies of AS but not others. You can even think of your score on the AQ Test as being like the Tom's Hardware Rating of your Coprocessor. (Lower numbers are better!).
If you lack that powerful social coprocessor, what can you do? Well, you'll have to run your social interactions "in software", i.e. explicitly reason through the complex human social game that most people play without ever really understanding. There are several tricks that a High-functioning AS person can use in this situation: