Splat,
You are right in that if the universe is expanding at a constant rate, the stars that are further away will be at higher velocity- and as expressed by the Hubble constant, the velocity is proportional to distance on the average.
However, astronomers have found that Hubble's constant is not constant as you go back in time. From Supernovae observations, they have determined that much earlier in the life of the universe, the universe was actually expanding more slowly than now- at a different Hubble's constant. So the presumption is that the expansion of the universe is accelerating.
From this they deduce that a dark energy with an omega of 2/3rds fills the universe and causes it to expand. Coupled with light and dark matter having a combined omega of 1/3rd, the universe is now thought to be flat and expanding faster and faster- at any given distance, not as a function of distance.
Hope that clears up this misinterpretation of faster and faster.

Regards,

Richard