Working in an outsourcing company I face different requirements from the customer side, including the need to screen the candidates themselves. Despite the reason of this is very clear to me, I cannot agree with this approach due to many reasons. Below I'll try to explain why I think that we should not indulge customer to interview employees before signing them on to the project.
To begin with no one knows your employees better than you. As a manager you have a long record of achievements and know the weaknesses and strong points about a candidate. You know the specific of the project and can match them against the qualities of the employee. So, you have all the means to choose the right candidate better than the customer. Involving the latter in the cycle seems redundant in this respect.
In addition to this, during the life we all learn the people who live in same area pretty well. Oppositely, we know near nothing of the people who live in a completely different environment, cultural and economical. What would you expect to learn about a person who come from the very different culture, having no possibility to read his body language correctly? This is a bad idea to screen candidates of different culture not having someone who can read the candidate effectively.
Finally, the desire to choose candidates is the sign of doubts in your qualification or trustworthiness, which is not a good thing for building an open and relationships between contractors.
In the conclusion I would like to recommend everyone to avoid involving customers into the process of selecting project teams, unless those customers have the profound knowledge of the culture, a good experience of doping reviews, and take your opinion of the candidates really seriously, so they can make a balanced decision. In most of cases, this is enough to just select the teams on your own. All the customers should care about is the result. And this is your responsibility to provide it, so you must have all the means needed at your disposal, including recruiting and hiring.