The overspeed checklist I refer to in the Boeing 737NG QRH is a memory checklist. It specifically says to correct an overspeed by adjusting thrust, and if necessary attitude. It does not say to use speedbrake.
Just a point of order. My QRH for the B737NG does not have 'overspeed' as a memory item. In fact it now has no actions at all! Also, there is a current bulletin titled 'Reduced Engine Response Times' that recommends the use of speedbrake when experiencing a sudden increase in airspeed, in order to avoid large thrust reductions.
The industry is quite dynamic & constantly changing, so it is often wise not to be too dogmatic about some issues.
I also agree with
LeadSled. A pilot who knows how to actually fly, rather than just manage, would know what to do in order to slow the aircraft down safely & should not have to refer to the printed word.