We just had our amateur draft, my draft scouts are 16 and my advanced is down to 6 (can only go -4 per season ) so I presume the omniscience of my draft gurus...  My amateur guys rated a relief pitcher at 76 overall so normally a guy like that would fully develop to something like 71-73.  After I signed my picks, my nub of an advanced scout rates his potential all the way down at 68!

With this configuration, can my player still reach the 71-73 relative to the "hidden" 76 (and "overshooting" my nub advanced scout's projection?)  Or is the player now forever bound to be a massive bust who is only going to get to 64-66?? 

Poor scouting can mislead you both ways, over-projection, and under.  His potential is going to be what it is, no matter what any scout says.

The higher budget is more accurate.

"Potential" doesn't change just because you're looking at it through a different budget.

So he can overshoot his 66 then?  The reason I ask is because normally I am familiar with the advanced scout over-projecting, like saying my 76 was really an 86 which he'll never reach. Normally it works the other way around, I thought.  I would be disappointed if my guy wasn't as good as my draft guy told me he would be

Yes.

Basically, every player has a set of hidden "true projections".  The scouting budgets apply some fuzziness to the projections you see.  A $20m budget applies the least fuzz to what you see; therefore, a $20m budget is the most accurate (though not 100%).  The further you get away from $20m, the more fuzzy (inaccurate) the projections are.

As shobob pointed out, the fuzz can either be understating or overstating the underlying true projections.  People tend to notice the overstated projections when the player turns out to never become the player they thought he'd be.  Nobody complains, however, when perceived projections are exceeded.  But those true projections generally do not change (unless he becomes a DITR).