I learned to solder electronic components by age 12, and later I ran an electronics operation where all of my staff could solder proficiently—they had to as bad soldering could easily have jeopardized the functioning of critical equipment. (Back then, anyone interested in electronics had to be up to speed with soldering or they couldn't do the job. Then soldering wasn't seen as a novelty or something unfamiliar as many of these posts indicate, it was taken for granted that everyone knew how to solder proficiently.)
That preface was necessary to indicate how vital hand soldering skills were to electronics and communication industries and to show that what I say next comes from long experience.
Bluntly, you're right to quote that text as not good advice as without certain stipulations it's very misleading; and that your own experience from using better soldering tools is exactly what is to be expected (it's the right advice). In short, don't use cheap crappy soldering equipment even as a beginner (you'll likely develop bad, hard-to-shake habits), rather buy the best you can afford. Moreover, one should not only buy a decent soldering iron with variable temperature control (or tips that work at different temperatures) but also it should support the wattage necessary to keep the tips at the correct temperature for the type of work you anticipate doing.
Same logic applies to your ancillary tools and consumables: use high quality solder with cored flux and always have a range of gauges to hand, always use 'solder wick', and or a decent desoldering tool, have syringes of flux† with correct size dispensing nozzles (flat-end/orifice hypodermic-like needles); and always have plenty of isopropyl alcohol (propan-2-ol) and suitable brushes for removing surplus flux/cleaning up (if it's unavailable then at a pinch use 95% or greater ethanol as a substitute).
I can't go into good soldering techniques here but I'll finish by saying always solder at the correct temperature and always clean (wipe) your iron's tips before use (and don't 'burn' them by leaving them switched on for long periods when not in use).
† There's different types of flux for different jobs—a flux, say, for reflowing IC leads on a PCB will use a different type to that used for soldering old components whose tinning may be slightly oxidized.