PNG alpha channels: what's the technical truth?

So what is the truth about PNG alpha channels?

google yields many photoshop forum posts declaring that “PNGs have no alpha channel, they only have transparency”
But I take this mean only that photoshop and most display programs only ever treat PNG alpha as transparency.

Pngs (at least png 24+transperency) must be RGBA images by my understanding.

Is there a way to manipultate the alpha in a png in more general ways
-like baking a greyscale texture map into it , etc?

or is there truly something unusual about png alpha that makes it impossible to treat them as flexibly as you might a 32 bit TIF or BMP?

hmmm
Super PNG plugin for Photoshop allows for this.
http://answers.unity3d.com/questions/327333/use-alpha-channel-for-specular-mapping.html

That said, I wonder how scriptable / automatable that will be.

Just write a PhotoShop action that converts layer alpha to a channel and visa versa. Then you can work with channels and reencode them as transparency. Remember that PhotoShop sucks for games work though. In this particular case I’m talking about PhotoShop’s behavior of tossing out the RGB data for any pixel that is fully transparent. Thanks PhotoShop. You’re a pal!