First to your concerns of possible fair lending concerns: agreed.
To Rick's comments, he makes an excellent point: if you can meet face to face, all the better. Consider it almost (almost) as a private or concierge banking service. Their needs are often much more detailed and slightly more numerous than a simple swap kit sitting in the HR Director's office.
Back to your first point though, if you are looking to cater to their lending needs, consider your prgrams very carefully. Doctors can be very mobile, so a amortizing or long term fixed product may not be attractive to them.
Additionally if they are a newer doctor or resident, their debt can be very high and their starting income may not be in proportion just yet... underwriting may need to be a little fancy for this, and pricing the risk will be inportant. Also keep in mind that not all doctors are created equal or are paid quite as lucratively as you may think... not all of them are making $250k right out of the gate.
I don't repeat gossip, so listen closely...