How does maximum speed vary with altitude? Question: How does a commercial jetliner's highest possible groundspeed vary with altitude (assuming wind=0) ?

My understanding is that drag decreases with altitude, therefore maxspeed increases with altitude.

This is also what Cpt. Simon Hardy, a B777 instructor, says:


  « Aircraft [referring to airliners] go faster at altitude than at low
  level. At sea level the aircraft [referring to a B777] can only do 330
  kn. And at altitude, 30.000 ft, it can do Mach 0.86. So it's a sort of
  sliding scale – as you descend, you get slower. » (source)
  
  



But today I read exactly the opposite on an aviation blog, which I found curious:


  « When a plane gets so high, you have to fly slower, since the speed of sound (and hence true airspeed for a given Mach number) decreases with altitude. » (paraphrasing, source)
  
  « Real basic point: You’re flying higher, you’re flying slower. You want to go fast […] you just fly lower. » (source)



... so which is it ?

The perfect answer for me would ...
• include a graph (Y: altitude, X: maxspeed)
• include citable references



EDIT (in response to the comments below):
I specified maxspeed as the highest possible groundspeed (assuming wind=0), although I'd rather prefer not to make that distinction, because from my experience this complicates the issue more than necessary: Of course the altitude will affect the different types of speed more or less, but isn't it nonetheless possible to make an approximate statement like "higher=faster, lower=slower" and explain why that is?

EDIT2
For a concrete example, let's assume:  


aircraft = B777
wind = 0 km/h (for argument's sake)
weight = typical weight of a B777 ~45min into a 9 hour long haul flight
aircraft has already reached cruising altitude


If at that point the pilot wanted to "get away" as fast as possible (let's say from waypoint IGARI), what altitude should be chosen?

Is the quoted blog post correct in saying that at an usually high altitude, the plane would fly slower, therefore it would have to go lower to fly faster?
This question isn't clear because "speed" means different things to different people, and this is also engine specific.  Every aircraft will have a different speed vs altitude profile.  In general...

Mach will go up, as you increase in altitude.  This is because the lower density air lowers the speed of sound (in an absolute sense).

True airspeed will go up as you maintain a constant indicated airspeed.  Conversely, maintaining a constant true airspeed will increase your indicated airspeed as you descend.

Normally, a jetliner should not be seeing true air speed at sea level.  For jetliners, even if your engines are good enough to get you there, the aircraft has an indicated airspeed structural limit that keeps you from accelerating.  You can keep the same speed (at structural limit) through higher altitude, which increases your TAS.

There is a chart here which should help show the relationships between altitude and speed:

A simplified chart for determining Mach number and true airspeed from airspeed-indicator readings: