I've found that the definition of what a DBA does varies from shop to shop. To be precise, however, administration of a database (particularly a complicated beast like DB2 or Oracle on MVS, things of that sort) is not the same as administration of the data model or the data within the database. I've done both tasks, and the degree of overlap varies from place to place.
Nonetheless, I would contend that normalization is really part of a data architect or data modeller's job, not a DBA's. Generally the DBA must contend with resource management: space, CPU, permissions, and so on. OTOH the data modeler has to contend with business rules, data integrity, and "turning data to information". The best results come from the two of them working together (or by one person doing both), but they're not really the same task.
As to the larger issue, well, I regularly work with people who are younger than the first program I ever wrote. Often I end up teaching them about new technology like XML, Perl (;-) I've always said the issue is not age, but how willing a person is to learn.