There is partly misunderstood information on both sides, like your statement.
With Li-ion batteries, it's not a threat of overcharging that is the problem (what it sounds like you are referring to), but dwelling at a high charge state. If you charge to full, unplug it, and let it sit on a shelf long term, that elevated charge state is still going to accelerate wear on the battery. Anything over about 75% can be considered elevated.
If you leave a phone plugged in, it's not likely to catastrophically fail due to the safeguards in place with the circuitry, just how a properly running refrigerator isn't going to go up in flames when left plugged in. What will happen is the battery will wear out faster if kept fully charged (my record was less than 6 months when I kept a phone plugged in at all times), just like how a fridge will wear out sooner if you set the temps at the coldest setting causing it to run more often.