Read what I posted again. I said nothing about leaving a signed copy in the doctor's office. I said "they [the FAA] can tell a copy from an original by the signature, without which it [the original certificate] isn't supposed to leave the doctor's office". IOW, the original is not supposed to leave the doctor's office until the doctor (or his/her staff) has seen the examinee sign it.
Yes, there is -- it's pretty easy to tell an actual pen signature from a copy of a signature. That's why when medical certificate is suspended or revoked, the FAA wants the original returned (same as with Airman Certificates).