Take the job - a job is better than no job first of all. It doesn't mean you have to stay there your whole life. The first part of the career is usually spent bouncing around trying a few things out...sorta like dating, plenty of flavours to try before you commit to anything.
Based on what you've studied you're obviously looking to follow the management route and that truly comes down in my opinion to hands on experience of dealing within an organisation and with people, both above and below you on an org chart. The more exposure you can get of that, the better off you will be. I wouldn't see it any differently than what you described as the graduate program you were looking for. Set your boundaries with your employer at the beginning with regards remuneration etc but also highlight the development side of things. Clearly they see potential in you and want to put you in a particular role. It isn't unreasonable for you to highlight this is something different than you were initially looking for, but you're flexible and interested and want to build a development plan with them so you can grow into the role.
At the risk of sounding like a really old basrad, don't fall for the illusion of company's being well run or that people hit management roles with the capabilities required. Most of what you have probably experienced until now is true in most organisations and there are a lot of numpties out there, so don't put yourself any lower than them

. Managing is really all about common sense, saying what you think needs to happen in a positive and constructive manner and treating people around you and those especially you are leading in the same manner you would like yourself. Keep that in mind and you won't go far wrong.