I guess anyone who teaches the historical approach to the bible in an accredited university I would consider a reliable scholar. They all believe Jesus existed...
I guess the claim that they have "residual attachments to Christianity" was a way of getting around the fact that the atheist and agnostic biblical scholars all believe that Jesus existed too, but they have a "residual" attachment because they used to be Christian?
It is hard to give one proof that Jesus existed at all, yes. You can do this with very few things in history, if any at all. If I say Pythagoras did something, I might have to point to a source from Herodotus, and you could rightfully point out that Herodotus frequently made stuff up. I might have to point to a source from Aristotle, and you could rightfully point out that Aristotle also believed Pythagoras was a time traveller, so is unreliable. There is no such thing as a perfect source, so historians have to work with what they're given.
A nice example from Jesus' life is the birth narrative. Only told in two (Luke and one other, I forget which) and the two accounts contradict massively. There are huge discrepancies in where the family travels, where it stays, why they travel, where they go after the birth, etc.
Why is this? Well the common point in both stories is that Jesus came from Nazareth, even though he was supposed to be born in Bethlehem. A fair conclusion is that Jesus really was from Nazareth, and the two gospel writers fudged making him come from the correct place and ended up with wildly implausible accounts that contradict on many levels.
The conspiracy position would be that both authors made up the story even though it has no mythical significance, accidentally contradicted each other dozens of times, but still conspired together to make sure their stories mentioned how Jesus came from a small town that nobody had even heard of at the time.