We faced the collectors vs. dealers issue a few years ago at another museum (not the NMNH), when we were writing our code of ethics. In fact, a number of people on this list kindly shared their thoughts and experiences.  

The consensus on amateur collectors who made no part of their income from buying or selling collections was: keep 'em, cultivate 'em, they're usually easy to bring up to speed re disclosure and conflict of interest issues, and they understand the collections-related issues of the museum in ways that non-collectors find more difficult. With some careful training (something every board member should get, initially and annually) and oversight, private collectors can be your best friends on the board when collections-related issues are on the table. 

The feeling on commercial collectors/dealers was more mixed. We opted not to put anyone already in the position of making a living from collections sales into board positions, feeling strongly that there is an immediate appearance of conflict of interest that would be difficult to resolve. We did, however, include some dealers on advisory panels, out of the policy-setting sphere. 

Sally Shelton Collections Officer National Museum of Natural History