I don't know anyone who's had difficulty being accepted to do a (non-science) PhD - it's the funding that usually presents the problem. Perhaps the person meant that Durham don't offer any MA or PhD studentships, in which case you'd have to fund yourself or get research council funding? Also, if a department has a bad track record of PhD students submitting on time, they can be black-marked for a period of time during which no students can apply for research council PhD funding. You can usually find this info out from the research council. But that would only be relevant if Durham were in that position, and if you wanted to stay there to do a PhD.

I'd be surprised if it made any difference to your chances of getting a PhD place. First, Durham has an excellent reputation. Unless their politics course is infamously bad, I can't see how that would count against you. More important than the institution you do your MA at are your undergrad and MA results, your references, and your PhD proposal. Do you know what area you might want to research into for your PhD? Does the Durham MA have relevant modules?

When my supervisor returned from a 12-month period of research leave abroad (during which we only had a handful of telephone supervisions and I didn't have a second supervisor or advisor), I submitted a short chapter. After 5 weeks of waiting for a response, I gently suggested that it would be helpful to have a supervision to discuss my work. He replied that I had slipped down his priorities since he had returned. (I hadn't exactly been high on his priorities while he was away.)