I've got to call bullshit on this.
Disclaimer, I'm a part time Minecraft mod developer. My understanding of this topic may have been unfairly tainted with unpalatable things like experience and and actual test cases.
modded minecraft takes 6+ gigs of ram to load in 15 minutes
I was able to load up the Monster modpack from Feed the Beast in about 6 minutes...and that included download the launcher, setting up authentication, and letting the launcher download all the mod files. Second run took 57 seconds to get to the main game screen.
I'm running with the default 2gb of RAM. Per the wiki, FTB Monster "currently also holds the record of being the overall largest Feed The Beast modpack, with over 200 mods included."
To put that in context, most "lite" modpacks end up with around 40-60 mods, and a "middle of the road" modpack has 100-150ish mods.
When running a "test" modpack that I've put together, it loads up in about 20-30 seconds, depending on how much debugging stuff I've enabled.
after that gives you mainly 1 frame every 3 seconds lasting up to a half a minute, with spurts of 10 frames a second for a couple seconds
If you've been playing for hundreds of hours, and have fully automated the processing, assembly, sorting, and storage of every block, item, and resource in the game, I'm guessing there will be parts of your game world that are so computationally heavy that it'll bring almost any computer to its knees. Granted, I've never seen this, and I ran a top 5 server back when Tekkit was the end-all and be-all of Minecraft Modpacks (there have been some huge performance enhancements since then), but I'm willing to admit that this could happen, however...citation needed on this.
how about vanella minecraft?
Well, how about it? Loading up the currently-latest-version of 1.8.7 takes a whopping 6.45 seconds to load, and runs at a nice stable 75 FPS without any tweaking of the video settings.
with the occasional one second lock up every few minutes
...you have no clue how java garbage collection works, do you. Please go educate yourself and then fix your settings. Better yet, just re-create the default profile, because it's already optimized for most use cases. The default "profile" that Minecraft runs under gives you 1gb of RAM, which is about perfect.
the joke has become "But can it run modded minecraft?"
Not really. Minecraft does have some constraints, namely the lack of a multithreaded server and heavy dependence on your CPU, but it's nowhere near "the joke" that you'd like to present it as.
on an i7-5820k and Nvidia GTX 970 with 32GB ram
All the tests I did were on a laptop running an i7-4870HQ CPU @ 2.50GHz with 16gb of RAM. Fairly beefy as far as a laptop goes, but nowhere near the specs dissy is claiming. If I'm desperate (or on a long airplane trip) I can get modded Minecraft running on my netbook, which is running a 1.6ghz atom processor and rocking 1gb of RAM. It's not pretty, but it'll give me 15ish FPS.
My only conclusions are that you're either you're doing it (somehow) very, very wrong...or you're intentionally spreading FUD.