There's not much to stop a crook being both officially well paid and totally corrupt.
A fish rots from the head down.
and
Power corrupts and absolute power corrupts absolutely.
and
Nothing disinfects better than sun light.
IMHO they all apply when dealing with public servants in unchecked positions of power.
Is it true? Well, maybe. From Van Rijckeghem and Weder (2001):
> ... we find evidence of a statistically and economically significant relationship between relative wages and corruption.... While economically significant, the relationship, nevertheless, implies that a large increase in wages is required to eradicate corruption solely by raising wages... The relationship between wages and corruption is not found in regressions with country-fixed effects which points to ineffectual wage policy in the short run...
I haven't found much better evidence than that, though there is Di Tella & Schargrodsky (2004) with a detailed study on a hospital.