I've repaired many tubeless tires with plugs (used to work in an auto garage while going to university) and it was VERBOTEN to plug a tire in the sidewall of an automobile, not to mention a motorcycle tire - the flex of the sidewall can cause the plug to fail, sometimes very quickly.
You did right to urge him to replace that tire, and the PO of the bike was almost criminally negligent to "fix" it in that manner.
I generally left a small bit of plug protruding from the tread area - as one rides it tends to get flattened out and helps to keep it in place. But, also not to leave alot sticking out or it will ride with a serious bump-bump-bump.