The question says that Eldon offers Rick the owl “in exchange for his secrecy as to the fallibility of the Voigt-Kampff scale”. But this is not what the novel says:
Rachael, leaning towards Rick, said, ‘How would you like to own an owl?’
‘I doubt if I’ll ever own an owl.’ But he knew what she meant; he understood the business the Rosen Association wanted to transact.
This “business” is not specified, so we have to deduce what Rick thinks it might be. My interpretation is as follows:
Eldon’s plan is to save the Nexus-6 androids by convincing Rick that the Voigt–Kampff test is not reliable. If Rick doubts the reliability of the test, he will not be willing to “retire” the androids, for fear of killing people by mistake.
The purpose of the blackmail and the owl is misdirection as to the nature of Eldon’s plan, in order to “sell” the unreliability of the test. The idea is that Rick should believe that Eldon’s plan was to save the Nexus-6 androids by blackmailing and bribing him into abandoning the mission. (This is how I interpret “business” in the extract I quoted.) If Rick can be convinced that this was the plan, then he won’t be suspicious about the demonstration of the test’s unreliability, as that will seem to be just an incidental element of the blackmail step of the plan.
The episode dovetails with the book’s theme of reality versus appearance: here we are misled on questions including the reliability of the Voigt–Kampff test; the humanity of Rachael; the nature of the owl; and the details of Eldon’s plan.