I am in no way affiliated with Longrifles Inc so I cannot speak to motives.
What I can tell you is mineral spirits does an excellent job on wax and petro based oils and grease, and requires minimal physical assistance, but it is a pertroleum distillate and may leave trace residue. Most people don't change the solvent in their parts washer everytime they use it so it may have some contaminants in suspension that would be left behind if allowed to evaporate. Soapy water would take care of those issues. Clean, dry, compressed air will greatly hasten the drying process, and is especially useful for drying joints, threads, the rough areas of the stock, and anywhere else liquid can cling, and there's no worry of it leaving lint behind.
Only you can decide if you want to go to this kind of effort, lots of people do good enough for them cleaning with various agents on a lint free cloth, they only have to please themselves.