Alchef - your starting post was referring to a lecture about valley flying and recces of Confined LS and specifically about starting from intowind and then turning to escape downwind.
There has followed lengthy discussion about constant speed, constant AoB turns (not the same thing at all) and some unhelpful mudslinging regarding physics.
I think the message your lecturer was trying to get across is that at low level, when using primarily external references to fly by, it is too easy to try and maintain constant groundspeed rather than constant airspeed. The result of turning downwind and subconciously maintaining the same groundspeed will always be a reduction in IAS, usually accompanied by an increase in power required to maintain altitude if you are the lower end of your speed range (as you often are when recceing or mountain flying).
All aircraft require more power when rolling into a turn compared to level flight at the same IAS so if you initiate the turn without adding power and you let the speed wash off (usually by letting the nose come up) you are quickly into a potentially dangerous situation, sinking towards the ground with reducing airspeed which could, if left unchecked, require more power than you have available to correct, especially at high DA.
At this stage all the theoretic arguments about frames of reference, inertia etc are not much use.
In a nutshell, if you want to make a safe turn downwind, especially in the mountains, think push with your right hand (you won't but it stops you accidentally pulling - and pull with your left hand so you add some power.