My dr's surgery has the same system where if you want an appointment the same day you have to phone at 8am. Usually by the time you get through all the appointments are gone.
There is one receptionist who really gets on my nerves. when dd2 was 3 weeks old she had really bad cradle cap, the HV told me to get an appointment with the Dr asap just to get it checked out, was really bad and was coming right down out of her hair onto her forehead, in her eyebrows and everything. So I phoned the Dr's and the receptionist said that I could have an appointment at the end of the week. I explained that it was for a newborn baby and that the HV had told me to get her checked out asap, but she said that I'd have to phone in the morning for an emergency appointment even though to her it didn't sound like an emergency. I duly phoned in the morning and got the same receptionist and got my appointment, but she did ask if it was an emergency so I said yes, she didn't ask what the emergency was though. This is the same receptionist who wouldn't give me an appointment with my GP for my 16 week check up because I should have phoned 2 weeks before to make the appointment, I didn't know that they had changed the system as I'm not usually at the dr's very often.
Last time I phoned for dd2 I got the nice receptionist who fitted us in that morning.
At my granny's Surgery the receptionists are all medically trained to assess whether or not you actually need an emergency appointment. I personally wouldn't feel comfortable telling a receptionist, trained or not, what was wrong with me. I'm phoning to see my dr and be diagnosed by them not a receptionist.
And as for the Dentists receptionist, don't let me get started. I'm quite happy to say though that she's just gone on maternity leave and might not be coming back, I'll try not to get too excited though until I know for sure that she's not coming back.