"I think we're better qualified than the assessors as we seem to have more empathy and are not doing the decision just based on cold clinical evidence."
What qualifications do you hold? Empathy isn't a qualification, it's a personal quality.
A judge and the panel at an appeal tribunal make their decision based on clinical evidence and asking the claimant questions.
If you don't base your decision purely on the clinical evidence yet you don't even communicate with the applicant, why do you think you are better qualified than the assessor?
It is absolutely fine to go by cold clinical evidence or, in the event that none has been provided, seek evidence from doctors. In any event, you have already said your decision is based on the PIP Assessor's report and, IME, they are often riddled with outrageous lies.
Thank God for tribunals. I would encourage everyone to go to a tribunal if they feel they have been underscored. Don't accept the slight changes made to try and pacify you following an MR. Everyone I know who has gone to a tribunal has won.