How to prove greedy algorithm for number partitioning?
There is nothing to prove about the statement you highlight. It is an empirical statement.

In order to have something to prove, you will need to formulate this claim formally in some way or another. There are many options, including average-case analysis, smoothed analysis, and restricted instances (which is what the statement points at). Until you have done so, it is impossible to prove or refute the statement.

The example given in your source shows that, in fact, the heuristic doesn't always succeed. Perhaps it gives a good approximation in some circumstances. The statement, unfortunately, doesn't hint at a provable claim which has any chance of being true.