A Bizarre Interview Request

Ms No Name writes with the following tale:

I applied for a job to a major UK philosophy department (top-10 in the UK). I was delighted to receive their invitation for an interview. The trouble is that the invitation came only 10 days before the interview (7 business days). I am a citizen of a non-EU country (not USA or Canada either) and thus require a visa every place I go, even for a short visit, even for 24 hours. Getting a UK visa requires collecting a slew of documents (normally takes me at least 3 days) and sending them off to the UK Consulate in a big city. Normally they return it with a visa in a week, but sometimes take longer. It was clear to me that 7 business days is not just cutting it short. It's impossible!

So I asked the department to interview me by video. I fully expected them to agree because I've had video interviews with other good UK departments in the past, no big deal. But this university said no. No chance. I pleaded - explained to them the situation, added my personal details (I have a toddler who would have to be left with a stranger babysitter for several days for this trip to happen). Nothing doing. The chair kindly and apologetically explained that they just do not interview by video. They gave no reason other than they just don't do it. They didn't offer to delay the interview either. Moreover they added they turned down other candidates just on that basis, that they could not arrive for an interview to the UK with 10 day notice.

Obviously I had to turn down the interview.

I am still baffled by the department's reasoning (don't they want the best person for this job? was I not a serious candidate to them?), but there is also the ethical question: did they have any obligation to give me a video interview? The more I think about it, the less sure I am...