I think you may have this backwards. In plain language:
Straight alpha: Stores the full RGB colour for each pixel, but ignores how transparent it may or may not be. ie the transparency of a pixel has no impact on the colour stored. This means for example if you render a white cloud with a soft whispy edge in a blue sky, the rendered cloud will only contain white cloud colours, the blue of the sky will not be present in the rendered cloud, even where the alpha transparency eats into the cloud.
Premultiplied: This simply means the image being rendered has already had the background baked into the rendered colour data. In the cloud example it means that it will start to turn blue as the edge of the cloud becomes more transparent.
In practical terms, straight alphas can be great because there's no bleeding of the background into the visual RGB data, you can take your white cloud and throw it onto any background you like, there wont be any blue from the sky creeping in. On the other hand If you place your premultiplied cloud onto an orange sunset background, youll get a blue halo around the cloud, which sucks.
However.... It isn't all roses. Sometimes you need the background colour to be baked into the transparent edge because some things are just flat out impossible to render due to the number of layers present or the motion on screen. Here's one which screws me over regularly; what happens if I have a 100% transparent plastic fan blade, but the fan blade is frosted. And in the middle of the fan is a bright red light. Visually the fan blade has the effect of looking like a swooshing darth vader light sabre. Its bright red and burning white from the brightness, but whats there? a 100% transparent object.... The alpha channel with a straight alpha will obliterate my rendering, its 100% transparent plastic. You can see it, but the alpha channel decides to ruin your day and now the rendering is useless.
The only option here is a premultiplied alpha where the background is baked into the motion blur and SSS of the plastic fan blade. Sure, I need to make sure my 3d background somewhat matches my intended compositing background, but its the only way to get any sort of useful render.
Same goes for motion blur, DOF blur, multiple transparent layers in front of each other (steam behind glass)
The honest answer is, use whichever one is least likely to screw you over. If you have lots of annoying transparent/blurry things to deal with, go premultiplied but plan your background ahead of time. If you want clean alphas on a simpler object render, go straight alpha.
I haven't read your linked blog all the way through, but I will say... there are an abundance of wrong people loudly proclaiming themselves to be fonts of all knowledge. Theres one in the octane community who insists on inserting himself into literally every thread on the entire octane forum to tell you youre an idiot for using a png file, he has 100's of blog pages which are a strange mix between 3d rendering and flat earth magical woo woo maths to show everyone just how right he is.
That said, your rainbow example does match up with what the blog says. The only difference is the blog seems to think the straight alpha is evil and you should only use the premultiplied, whilst I would say both have their uses, with straight being preferable when possible.