Let's keep this in perspective.
Tom Barr is highly trusted and has set up more tanks and experimented with more tank setups(plant types, light levels, ferts, low light, high light) than any of us ever will. Anyone new to the hobby should, therefore, seriously look at his methods and recommendations.
So, how does this relate to James list of low light plants? We can argue based on our individual experiences that some of the plants on the list may or may not be the best choice for a low tech setup, but this does not negate the value and validity of setting up a low tech, low light setup, with proven low light plants. No experienced hobbyist would ever argue that plants in such a setup my not produce huge lush leaves, or grow at astronomical rates like those grown via high tech setups. However, there are many individuals new to the hobby that don't want to mess with EI fertilization 3 times a week, invest in expensive c02 equipment, perform 50% water changes weekly to prevent excess build up of ferts, and continuously trim plants just to keep plants from choking out their tanks. And while light may not be the only contributing factor to algae, I have found from my own experimentation that it is a huge factor. Just try it yourself. Put a bunch of plants in a tank, bomard it with high light, use no c02 and no ferts and watch the algae farm that emerges. This relates to the point that you would be hard pressed to find algae issues to that extent in a low tech tank. You may end up with some diatom algae and green dust algae at the beginning and perhaps some black beard or black brush algae, but in my experience this algae seems to die back in a low tech tank and disappears as the tank matures.
I have two tanks. A 40 gallon high tech with all the bells, toys, and whistles and a 5 gallon low tech setup up(no c02 14 watts daylight pc lighting, and daily dosing of excel). While the plants to grow at an insane rate in the 40 gallon, it is a real PITA keeping on top of the maintenance chores to keep the tank from crashing. I also have a 15 gallon high light, DIY c02, with ADA Aquasoil II. The SAE and Kuhli loach are alive and kicking, but again, it is a PITA, with respect to maintenance because the plants grow extremely fast and I have to keep on top of weekly water changes. In comparison, the 5 gallon is a piece of cake and I am quite happy with the growth rate and the fact that it is very low maintenance. Unlike the 40 gallon and 15 gallon tank, there is more room for neglect with the 5 gallon without issues, not that I would neglect it. The tanks are all algae free and the creatures in all the tanks appear healthy.
If I could do it all over again, based on what I now know and learned from setting up different tanks, I would go low tech, low light with low light plants instead of going high tech. For me, the trade off of having slower plant growth with much less maintenance is well worth not having to ensure high maintenance on a tank to keep it from crashing.
I credit Tom Barr for sharing his low tech approach and would advise anyone new to the hobby, who just wants to grow some plants without a lot of fuss to check out his method. It may not be the only method of setting up a low tech, low light tank, but in my experience it works really well. Choose plants from James excellent list and set up as per Tom Barr's method and you may be surprised as to how easy it is to grow plants without a lot of fuss or trial and error.
P.S. and as a side note.
I have a co-worker who is not into planted tanks. He has some java moss in his guppy breeding tank and uses the "stock" lighting(yeah you heard it right, the stock lighting that came with the tank). He takes no special measures, uses no ferts, has only plain old gravel and the java moss is lush green and growing like crazy. We have the same tap water, we have purchased the moss from the same source and I even tried a sample of the one grown in his tank, and I have tried growing the java moss in both my high tech and low tech tanks without success. It starts out green, then gradually turns brown and dies. Go figure. So, yeah it is possible to grow certain plants with only stock lighting and no special requirements whasoever. My co-worker is living proof of that.