Whilst I understand what you mean, it would be more correct to say that the only provider approved to conduct the DVLA test are Specsavers.
Hmm - It wouldn't be correct (if someone 'failed' the test) that they couldn't have an opportunity to appeal and have a second opinion.
Opticians can get it wrong. My daughter and I both had eye tests (at the same place) - It was only when we had difficulty with our new glasses (at night the 30 sign could be 30 or 50 for me!) that it became apparent. We had to pay to have retests at a different optician, who was very reluctant to do them (protecting the profession?) and we then had great difficulty getting refunded by the first optician, who was adamant there was no issue. I won't state publicly the names of the establishments.
It is always the case (over all the years I've worn glasses) that once the glasses are made they are just checked for frame fit, but never tested using the chart!