I could not agree more.Definitions such as the one above don't make sense and that seems to be the reason why the person who wrote the opening post got confused. The concept of field lines, though useful, has shortcomings that don't seem to be realized by the people who write the bad definitions.
When one represents the field by drawing "lines" (which I shall continue to call flux lines!), they are always distributed so that their density is proportional to the local field strength. There is nothing within the definition of a"field line" that requires this constraint, and without it they show only the local direction of the field...not nearly so useful.
I truly don't understand the controversy here.