While identifying prospective independent board members will help make VCs slightly more comfortable investing in your startup, they may still be concerned about getting an independent approved.

Selecting independent board members is often done by a process of mutual approval, whereby both the directors representing the management team and the investors must approve them.  This selection process is designed in spirit to ensure that the independent director does not favor one side or the other (they should remain independent of the influences of either party).  Nobody wants the other side to have a ringer. 

Since independents must receive mutual approval be to be accepted, VCs are sometimes concerned that the management representation on the board will choose to block all of the proposed independents leaving the company with an even number of directors and no mechanisms for breaking ties in the future.  While this doesn't happen if all parties are acting in good faith, being a good partner is not always a high priority for individuals. 

As a result, VCs may seek to insert penalties in the term sheet that incentivize the management side of the board to select an independent director.  These terms might include something as aggressive as the VCs taking control of the independent's board seat after a designated period of time until an independent is selected.

In sum, it's important to VCs that your company selects an independent board members.  Typically this comes about through a good faith effort by all of the parties.  VCs that have had problems securing an independent director in the past, may look for mechanisms to ensure that the management team actively works to find and approve this person.