I'm a qualified Classical Yoga teacher and have had T1 for ~20 years. I have a particular interest in Ayurveda, the 'health science' aspect of yoga. The literature of this tradition predates the distinction between T1 and T2 in our terms. I asked an Ayurvedic master about his claims as to the benefits of this tradition for "diabetes" and it was clear that he didn't differentiate between the conditions in the way that Western science does, though it was evident that he was talking primarily if not exclusively about T2. In Yoga, what we call T1 would be seen as a Pitta/Vata imbalance, whereas T2 is a Kapha imbalance (Pitta, Vata and Kapha are two-part composites of particular elements: fire, water, earth, air and space). Just like there are common treatments for these conditions in Western medicine, there is overlap in Yoga (e.g. both benefit from lower GI diet and from regular exercise - more-so for T2). Some of what is recommended by Yoga for these conditions is consistent with current Western medical advice, whereas other aspects are decidely more esoteric. As to whether asanas (the postures of physical yoga) can benefit T1, I agree that the exercise itself can do the same as any equivalent exercise e.g Pilates by lowering BSLs at the time and for a while after, plus increasing insulin sensitivity if the exercises are done at a sufficient level of intensity, duration and frequency. T1 patients with a higher Pitta (fire energy - which Kate certainly has - I should know - I'm the same) will benefit from the exercice more than would those with higher Vata (air/space). Pitta patients would benefit more from an asana regime that is a decent work-out but doesn't get them too hot (Bikram yoga would be very bad for a pitta patient as would Ashtanga if too vigorous or in hot weather). Vata patients need less movement and more focus on strength and stability, with lots of floor-based work and lying down (increases groundedness) (some forms of Iyengar can be useful if there is more focus on strength than flexibility). Any postures and practices that are calming will benefit T1 (lowers cortisol which improves insulin efficacy). Yoga nidra (the guided meditation done at the end of some asana classes) will be particularly useful. Twisting asanas are said to be good for the adrenals and liver/pancreas. This isn't about squeezing non-existent insulin out! To understand why the twists would work, think more along the lines of TCM and its meridians (as in acupuncture) (which in yoga are called nadis). The full explanation as to why this approach works (or can work, as one size doesn't fit all) is best obtained from a skilled practitioner or relevant text.
I reckon there might have been a bit of a pitta dynamic going on between Kate and her new yoga teacher. The teacher clearly has the 'I can fix it/you' attitude typical of some pitta people (self included), and Kate is rightly sceptical/defensive of his relatively intrusive 'I can fix you if you do what I tell you' approach. He also evidently isn't T1 or he'd likely understand that unless we're dealing with a particular problem arising from T1, I suspect most of us would rather deal with anything other than T1 (as it takes up enough of our energy etc. and some times, more attention only makes it worse). Kate is saying in effect "it ain't broke in a way that I believe you can fix" (and his approach seems generic and doesn't appear to recognise that fiddling with the pancreas isn't going to fix an autoimmune disease). I'd likely have asked him how his focus on the pancreas can address the underlying cause of the disease (I think I know where he's coming from but it warrants explanation). But he's right about being able to potentially improve ease of management by working on aspects of the endocrine system. Doing this is a treatment for the condition but is clearly not a cure. Even a 50% drop in insulin requirements is still not a cure, esp. when maintaining this benefit requires adherence to a considerable physical, mental and likely spiritual regime (with dietary adjustments that are themselves often a challenge).
I suspect that he interpreted Kate's apparently "short" response to his offer of assistance as evidence of Kate having a pitta imbalance (thereby simply reinforcing his view that he can improve her T1, which he might be able to do by addressing what he sees as excess pitta, itself evidence of a major factor in the yogic view of T1 pathology).
Wondering how I would have reacted in Kate's shoes, having likely attended the yoga class for exercise and relaxation rather than thinking of it as a medical consultation. I'd probably have done much the same: "Thanks mate but it's under control. If I feel the need to fiddle with a regime that's working, I'll let you know".
A bit of a test of his cred' would be to see if he'd offer a free private class to train you in the asanas that he recommends (complete with an explanation as to why they would have these benefits).
As a teacher, I wouldn't have followed up the offer (which I probably would not have made until I knew the person better) and subsequent rejection with an email to a new client. I think that's overstepping the boundaries of professionalism, even if it was well-intentioned. It feels a bit like cold-calling to me.
Everything goes somewhere