No. Depending on which game we're talking about, you can play on laptops...I play aapg on a 2011 Samsung rf511 laptop (it had a beefy CPU, but everything else is average to scrappy, including the screen which is sort of poor). The real issue on laptops as always is how heat is dissipated, and whether or not the psu will properly cope to the load.
There are also some 3rd party tools that disable part of the rendering "features"(I think some used them in the past to deal with the early netbooks lack of power), so to speak, such as lighting or textures, but aside of the game looking crappy, tools such as that won't be allowed by Punkbuster.
But actually, even my old Asus netbook I had several years ago was nearly able to run AA2 somehow, so I bet you guys must be running on truly ancient hardware or either have a lot of bloatware running in the background aswell...
Most of this is true (I've personally run AA on a laptop with onboard graphics back in ~2008), however the crappy screen is most likely a benefit to the performance before anything else.
In any case, first thing to try (as has been stated) is to lower all your graphics settings to the lowest possible ones. It helps A LOT.
I didn't really look at the post mentioned, but I know some of the old performance tweaks could also be used to gain an advantage over other people so they might not be allowed with Assist. Most of them will probably just be CVARed (meaning you get kicked and are not able to play with the settings), but some of them might warrant further action (some settings have consequences not intended at first, but something that can be exploited). But again, I didn't look at the specific post.
Also, (and I mean no offense) if you're getting 15 fps on Bridge (on of the easiest maps on fps), your system must seriously be weak.