@7120 - reading over the CAA guidance I don't see that the AME would necessarily need to have access to the fancy equipment themselves, though many may have access to a slit lamp (I do, though I'm neither an opthalmologist or an AME).
If you have documents to detail your uncorrected visual acuity at one point in time and that your cornea has been examined by a professional, then it's well within the capability of an AME to check your vision with a few simple aids if there's a gross change since the last measurement, this would be a trigger for further investigation. If your vision was well within specifications then why not clear you for VFR day flying?
My own experience - saw a taxi driver whose vision had apparently been recently been checked by an optometrist and pronounced 'okay' who was well outside the limits for professional driving.
At the end of the day you shouldn't be able to force anybody to sign a form - either comply with whatever seems acceptable to them, or find someone else to sign it.