Why are noble metals more electronegative then most metals?
The noble metals are defined by a resistance to oxidation and corrosion, and this should not be interpreted as a lack of reactivity, but instead an aspect of their high EN.  So, there is no contradiction as you seem to be thinking.  Basically, they hold onto their electrons better than other metals, so it is harder for acids and oxygen to steal electrons from these metals. 

The noble metals are generally considered to be ruthenium, rhodium, palladium, silver, osmium, iridium, platinum, and gold, so I'll mainly be addressing these particular elements. There are a few reasons why they should have a higher electronegativity:


The lanthanide contraction causes these atoms to have a higher than expected $Z_{\text{eff}}$. This means they hold on to their electrons tightly, so have higher electron affinities and ionisation energies which corresponds to a high EN. This doesn't carry into group 12 because accepting electrons for these elements would result in adding another energy level, so it's not as favorable.
The filling order: By period 6, the 6s, 4f, and 5d orbitals are all so close in energy that the filling order changes, which affects the properties and chemistry of the elements.  Notice that almost all of these metals, apart from Os and Ir, break the typical filling order. Adding electrons to these atoms therefore does not have the same effects that are dictated by normal periodic trends.  
Relativistic effects - Somewhat related to filling order. By period 6, nuclei are so heavy that the core electrons are moving close to the speed of light.  This causes a contraction of the s orbitals, the inert s pair effect, and other things that have a big effect on the electronic structure and chemistry.


Also, the noble gases start becoming reactive around Kr, and more so for Xe, because they are so big with such high shielding that electronegative atoms are able to take electrons to form bonds.  Some people get confused about this because they think it's just Kr, and Xe being weird, but it's actually a trend and continues with Rn, but there isn't much data on Rn compounds, or much use for them, since Rn-222 is the longest lived isotope with a half-life of ~3 days.

Periodic Trends of Transition Metals could help explain some of this.