First question is why is this Doctor talking with you in the first place since he seems to be convinced that the previous detailer knows it all? If he liked the work before why would he be considering jumping ship? There has to something that was less than perfect for him to be shopping. Even if you approached him, if he was completely satisfied he would have said so and told you "good day". The fact that you did not sell him in the first go around could mean it's too late already. If you come back with more reasons now he will wonder why this new information was not presented when you first talked. If you do get the opportunity he may question your sudden found knowledge.
I will tell you from experience that Doctors in general may have the money to buy these fancy toys, but in general their attention to cleanliness stops with their work. Some of the dirtiest vehicles we get are from doctors. Their minds are busy with other stuff more so than their cars. Please note in many doctors cars we have found needles and drug samples laying around. Be real careful. I do not know if they are just absent minded, slobs or entertaining themselves.
If you have the opportunity to show this person your work, that is what it will take. On many customers I have them pull in and polish a corner or some small area to show them the difference. If they are nervous I show them something on either my vehicle or one that may be in process in the shop. Getting past the wonders of clay may be difficult as there are many people that think it is the end all for paint finishes. While it has a place in our business I do not clay every vehicle or clay then wax with out some type of polishing taking place. It is a tool used to remove surafce contamination and can be used to microfinish paint, but the paint while feeling smooth, will still need either a foam rotary finish or at least dual action orbital polish in order to remove the marking the clay will leave. If you read the small tips in any Griot's Garage catalog they tell stories of show car owners claying their cars paint then wiping his show car brand of wax over that and they win every time. The problem with these type of articles is that they forget to mention that these are """SHOW CARS""", not daily drivers. These people do this moments before the car is seen or right there during a show. Any wax looks good for the day. It will also cover up most marks for a short time. After the show the cars are either trailered or driven straight home and locked up until the next show. Far from realistic usage that the rest of us deal with. Put these outside for a week or two and drive them to work and back and you'll suddenly be able to see that micro marring the clay leaves under that great wax as it evaporates under the sun and rain.
Be very careful with this customer. If he has this many reservations about what you have told him you can do then it could be a very bad experience for both of you.
Regarding the comments of not telling customers what your process is works only when they do not ask. If you are asked about the process you could not take a polisher to their vehicle knowing their concern without permission. That is just asking for trouble. Come on guys, lets be professionals, not disclosing your procedures because you know better than the customer does little to raise the bar in this profession. If your customer tells you they heard bad things about buffing, you need to address the issue up front by example or knowledgeable conversation. Never would you go ahead and buff the car knowing their fears and thinking you'll just prove them wrong. By experience, training and keeping to a higher standard you should be able to convince the customer that your system is the best way for them to take care of their car. If this cannot be done upfront it is much better to turn the business down in a professional manner, than getting into a sticky situation later.
Here is a perfect example. I had an attorney call me and say he needed a detail. He then went on to say that I will remove his wheels and clean the back sides, I will remove a seats and clean underneath, and that I will use the wax that he will bring me and hand finish his vehicle. I took time to explain my process which did not include any of the above. Reasons being high liability if a lug nut or seat bolt cross threaded and broke or stripped, plus I explained that no amount of hand polishing will end up as even a result as what I can accomplish with my machines. He listened and then repeated his demands. I sincerely thanked him for calling me and told him that I felt it would be better for him to find a business that was willing to do the worked his way. That was two years ago. Apparently he never got what he wanted as came back to me. He never tells me how to do his work any more and brings in his 4 personal vehicles and recommends all his friends. Who says the customer is always right? You have to know enough to tell a customer NO and turning down business can be the right thing to do.
Just my thoughts.
Good luck!!!