My instinctive reaction to this excerpt was 1) board member fundraising involvement is way too often ignored by many nonprofits, which is a debilitating mistake, and 2) to be concerned about how this cardinal rule could be used to keep people without financial means and powerful connections from serving on nonprofit boards when they may actually have quite a lot to offer an organization. I do agree that board members should absolutely be key members of the fundraising team and should know involvement with fund development is an expectation of their service.
So with those thoughts in mind... There should be an expectation each board member will make a gift that is significant in accordance with their financial means. They will be given the training needed to make them confident in identifying, cultivating, and/or approaching other potential donors (individuals, foundations, etc.), so that, with their particular strengths, they can best contribute to the financial sustainability of the nonprofit. If members of your board aren't contributing in these ways, then you need to get a new board. If your organization is unwilling or unable to provide board members with the guidance and training necessary to be successful, then you need to take a hard look at your organizational culture.
The above "rule" is aligned more closely with the realities of small and medium sized nonprofits who may not be able to attract particularly wealthy board members.* This rule is also better in tune with the philosophies of grassroots groups, social service organizations, and other nonprofits who may be more concerned with having board members that are representative of the population they serve or the cause they seek to advance. Even for those nonprofits, though, it is imperative board members step up to keep the organization financially afloat, so training and guidance are important. If a board member is going to be asked to do something then it is only fair the expectation be upfront--everyone on the same page, eyes open--and the tools be provided so they can do the job well.
*Note: Don't be afraid to ask! You never know what the response will be. Stay tuned for a future post on being confident in the worthiness of your nonprofit.