Side note: BRHSM (OP) is refering to Geek Technique #12 in issue 222 of Computer Music magazine.
Great question, BRHSM. I have three answers for you, but only one is true. I'll let you come to your own conclusions. :)
Option 1: I must confess, the video is one big deception.
Everyone knows that filters always reduce amplitude and increase available headroom, without exception.
Weeks of planning and editing went into conjuring the illusion that high pass filters often cause an increase in amplitude.
I did it so that I could provide false evidence in arguments against people who I secretly agree with - and I would've gotten away with it if it weren't for you meddling kids!
Option 2: I made a foolish mistake. Steinberg and iZotope's software misrepresents waveforms, frequency spectrums, filter curves, and amplitude meters - everyone knew this except for me.
Also, the staff at Computer Music have no common sense. They add fools to their experts roster and print wild assertions without fact checking.
Option 3: The video is accompanied by a 2-page article, which includes ~600 words of info that's not in the video to help you make sense of it all. There's also an email address so you're welcome to send your questions to me directly. :)
The point of the piece wasn't to discredit all uses of high pass filters. I specifically oppose the habit of blindly highpassing, hoping to save headroom, without checking before/after for tonal shifts and any unwanted increase in headroom.
The myth is that filtering always reduces amplitude - it doesn't. I showed that it doesn't using test signals, then I showed that it doesn't using musical signals.
Anyway, you asked why this is happening. You might want to review the video, but basically a complex waveform is made from multiple frequencies - sines. If you alter the amplitude and/or phase relationship between those frequencies, the waveform will change accordingly.
It's not an easy concept to explain clearly in words, which is exactly why we made the video. One way to think of it is to imagine that some of the frequencies are being 'clamped down' by some of the other frequencies - so reducing certain frequencies may reduce the 'clamping effect', thus resulting in an increase of total amplitude.
You also asked how this will affect complex lead sounds. Again, I'd ask you to refer to the article, but for the sake of giving a complete answer; it'll probably make them take up more headroom, it may even have a negative impact on the timbre as well.
By the way, Michael Hansen Buur's fantastic answer raises the important distinction between traditional mic'd sound sources and virtual synths. I didn't get into that in my article, but in any case here's what you should do:
1) Measure the amplitude
2) Add your high pass
3) Measure the amplitude again
4) Make your decision
It really is that simple. The point of the piece was that we should all engage in critical thinking instead of blindly doing what everyone says we should do. Just don't apply the filter unless you're satisfied it's doing what you want it to do and nothing else.
By the way, if you're into making modern/electronic music, there's an email course on making mixdowns easy starting at the end of the month, totally free to join. Head over to www.owenthegeek.com and enter your email address.