What I kind of find surprising is that people are surprised that a 'fan' can do a better job of restoration than a company with (seemingly) endless resources.
The truth is that a fan with the right background and training would often be capable of doing a 'better' or to be more accurate, a more 'genuine' job when restoring a film.
The tools that the pros use are available or can be programmed, film scanning, though hideously expensive (I just got a quote of USD$25,000 for two hours of 35mm to be scanned) is available.
The main differences between a Disney restoration and a fan restoration are mostly twofold.
1) Familiarity with the source. A Disney employee may have a deep understanding of the film, or a passing interest. They may have been alive and immersed in film in the 1970s or they may not have been born in the 1970s. They may have access to original costumes and models, or may have never seen them.
The 'fan' might be old enough to have experienced the 70s films and aesthetic at the time of release (I sadly am more than old enough), have spent more hours than is sane watching the films *on film* and spent 1000s hours pouring over models, costumes and reference materials. They can remember the experience in the cinema, the way the audience gasped and cheered and stood and applauded. Where they laughed and where the cinema was dead silent with anticipation. They have viewed every damn frame of the film countless times, and sometimes are surprised to realise that there is no audio, as they have been hearing it even when playing back the sequences in silence. They know every character, every blink, every nuance of the film. This makes a difference. They know just how important to the story that little flash of colour on the stormtrooper's costume is. They know that the snaking cable at the corner of shot should be hidden in shadow, and that the highlights should be singing in Carrie's eyes. They know the film, on a level that is hard to understand if you haven't been living in its frames for the last decade or so. You won't make the mistake of balancing out the blue-green of the Death Star's walls to a neutral grey.
It isn't just another cleanup job that you have been assigned to for the next two months.
2) Time.
Stupidly large amounts of soul eating time.
The fan has the ability to spend a day, a week, a month, two months on a 10 second sequence. And then revisit it again later when a new technique gets invented for a different sequence that may give a better result on an old one. You get to agonise over whether the smearing on the stars in the background in this shot is lens coma (leave it in) or channel misalignment (take it out). You get to experiment with techniques like image stacking, deconvolution, light diffraction remodelling and other tools that come from diverse image processing fields, but aren't in the standard 'film repair' product ranges.
Also time to track down people and references and write programs and source equipment etc. etc.
None of this time is really available to a company, no matter how much they love the film. It just isn't economically viable, and has limited usefulness to the general movie buying public. How many customers will really care that the starfield is misaligned by half a pixel, or that the colour of the wires inside Threepio's torso are not consistent from shot to shot?
It just isn't worth it, even to a company like Criterion to spend years on this stuff.
So in short, with the right background, horrible amounts of time, a good skillset, a bit of luck, and flushing most your spare money down the toilet, you can surpass some of the best restorations out there, you just have to give up a large chunk of your income and spare time to it, know what you are doing, know what you don't know, learn, improve and work damn hard.
And have a bit of luck :)