like most archaeological and historical finds, they are mainly guessing...but it makes for a fun story 
Um..no they aren't Dude, modern archaeology relies on scientific evidence. And the bottom line is that experts are experts for a reason. If a significant number of them agree on something then they are probably right. If a single piece of evidence had countered what they found it would have been game over. They would lose their entire academic credibility if they made a claim for something they knew to be untrue.
Great programme. The face recreation was a pile of pony but rest was very interesting. My favourite bit was when the mad lady wanted to cover the box of bones with the King's standard and the clever scientist lady said she didn't want to do it, quality look on her face when she said it.
I actually thought it was a bit dumbed-down with not enough time devoted to the science and the historical context and I didn't like the presenter one bit but Philippa Langley was the highlight for me - amazingly dedicated but totally potty, bless her.
I quite agree with the you about the bit with the standard, but the best bit for me was when she got all teary in the lab. The osteologists were looking at her like she'd gone completely bonkers! 
I'm not sure the reconstruction can be dismissed entirely. The woman who does them is the absolute expert at it and has remodelled unknown murder victims that have later been identified. Given that she had near contemporary portraits to work with, she actually had more information than she usually does so I'd say it was reasonably accurate.