Last Night's TV: Katie: My Beautiful Friends, Channel 4; Bible's Buried Secrets, BBC2

Two years ago a stranger threw acid in Katie Piper's face and now she's reduced to begging. You could see it made her uncomfortable in Katie: My Beautiful Friends, a follow-up to an earlier documentary about her recovery. It can't be easy asking people to give you stuff and she had to take a deep breath before picking up the phone to Moët & Chandon to ask them whether they would be the champagne sponsor for the launch of her new charity. "We might have to do bring a bottle at this rate," she said, as the phone rang on and the voicemail didn't cut in. Perhaps Moët & Chandon were hiding. I expect they get touched up quite a lot for champagne sponsorship. But I hope someone answered the phone eventually, because Katie deserved the backing.

She's raising money to set up a scar-management centre in Britain, similar to a French clinic that had helped her regain enough mobility to make her face expressive, rather than just a mask of survived damage. It worked well enough to permit her a lovely smile, which considering what had happened to her, occupied her face for a startling amount of time, only briefly knocked off when she got a telephone call telling her that the man responsible for mutilating her was appealing against his sentence. One imagines she has quite a few such bad moments – and times when the resilience and courage falter – but overwhelmingly here she was putting on a brave face, a cliché that has a sharp edge to it in the case of those with conspicuous disfigurements. If they want to lead a normal life they don't have any other kind of face they can wear.

Adele, one of the two young women that Piper visited to share experiences, isn't facially scarred. In fact, she's strikingly pretty. But, after she had an epileptic attack while she was in the shower and knocked the tap to scalding as she fell, she was left with severe burns on her arms and body, and badly damaged in confidence, too. "I feel a lot of the time like I should be at the bottom of the heap," she said, confessing that while her contemporaries were teasing each other about not having lost their virginity yet, she was still waiting for her first kiss. Her story, like Katie's, appeared to be travelling on an upward trajectory, concluding with her performance in an Edinburgh fringe production, which required her to showcase her scars in front of an audience of strangers.

It's almost certainly insensitive to compile a league table of adversity, but you couldn't help but feel that Chantelle, a young woman suffering from arteriovenous malformation of her nose, had a far bigger challenge. During childhood it had been a negligible birthmark but as she aged it grew, unmissably central. The language of beauty is easy – one or two words will do it, and none of them hurt when they land. The language of disfigurement is not, since any metaphor that does justice to the difference is in danger of causing more pain. So it's enough to say that you had no difficulty in understanding why Chantelle might succumb to a panic attack in a crowded shopping mall, or why she was prepared to endure gruelling plastic surgery to look just a little more ordinary. She also had hard proof that adults are capable of being as cruel as the schoolgirls who'd tormented her during her teenage years. On a recent trip out she'd been assaulted, verbally and physically, by a drunken woman enraged by her mere presence. And, though it may be trite to say it, no physical disfigurement could come even close to being as ugly as the attacker's mental one.

It would be improper to mention Dr Francesca Stavrakopoulou's looks. Clearly whoever commissioned a three-part series on Biblical scholarship for BBC2 was entirely indifferent to the fact that it would be presented by someone who looks as if she's shimmied out of one of the hotter passages of the Song of Solomon. I imagine they didn't even ask to see what she looked like, only a list of her academic publications and, perhaps, a confirmation that she had a good writing style and a reasonably clear speaking voice. Anyway, whatever the process the result is distinctively interesting, essential watching for anyone interested in the finer points of ancient Hebrew theology and pretty intriguing even for those of us who aren't.

She does overegg things a little. She started last night's episode by saying that she was going to explore an idea that "rocks the foundation of monotheism to its core", by which she meant the buried evidence that the Israelites had only gradually moved from polytheism to monotheism. To a non-believer this seems so self-evident that it barely needs stating. How else would it happen, after all, short of blazing revelation from the God we don't believe in? And while it's true that devout Jews and Christians would have more difficulty, the more sophisticated of them find it child's play to reinterpret awkward phrases so that they tally with what they now believe. I don't think her film will have knocked even a grain of sand off the foundations of the faith. It was interesting, though, to see how the evidence had been buried by tactful translation, and how much of it still pokes above the surface. Interesting too to hear her talk throughout of the Bible, as though it was a single book rather than many bound together. That's literary monotheism, I think, when polytheism makes more sense.