Most of simple statements that can be stuffed into one sentence are generalisations, and if you take them out of that context, they will be misleading.
I have been channeled as an Old soul and I keep my house clean, because I like it that way. Dirty house drags me down. Same with clutter. That being said I had periods in my life when you could not see my rooms floor and you would find some disgusting things in there (upto adolescence). When you live in your parents house and you know you are not solely responsible for its state, its very different than having your own place . I also (much later) had a period of a few months when I did things like cleaning tops of refrigerators. It did not last very long though.
I had a period in my life when I cleaned for company and I sometimes still might do that. More like put things away, if needed, than clean. But if just one person comes for a coffee and I happen to have a slightly messy kitchen, well as long as I am able to make a coffee, who cares?
So when they say that Old soul does not bother shoving anything away, the way I understand it, is that they are expressing "take me or leave me" attitude (but physical age and imprinting can mess with this).