Does iron really sharpen iron?

The metaphor necessarily means that different persons have different qualities and by sharing those qualities they can become sharper!

Iron in its pure form is rarely manufactured or I can safely say that is NEVER manufactured. All the different specimens or even the different parts of the same specimen of Iron are most likely to have a different composition(Especially Carbon Concentration) at some level of precision. So if the the two specimens do have different compositions then their hardness values are different. So it definitely is possible to sharpen a piece of Iron by another of a different composition.

Now considering the Ideal case where two pieces do have identical composition, there comes temperature in action. If one of the pieces is heated up significantly, it becomes ductile and hence can be sharpened by the other one.

Again, two pieces with exactly same composition and temperature can have different hardness due to the number of dislocations or mechanical working imparted on them...

So by all means.. YES! Iron does sharpen iron.