I don't think that it's entirely accurate to say that "going to a lower university will not restrict your chances..." I suggest that it's not realistic to suggest that graduating from, for example, Bedfordshire, won't restrict a person's chances when compared to graduating from, for example, Cambridge, or UCL, or Manchester.
Even university-blind recruitment may cancel out the competitive difference between a candidate from a well-resourced university with demanding entrance requirements and academic standards and a university with small resources and relatively lower entrance requirement and academic standards.
I don't think that students should fixate on a small group of universities in the belief that, if they don't study at one of those universities, they will have no chance of career success, but at the same time students should have a realistic view about the probable qualitative difference between a more selective university and a less selective one.