But is it possible that people lose their teeth because of other factors like poor diet or lack of money to take care of their teeth (and the rest of their bodies) and dementia would really be related to these other factors?

It's a very good point and entirely possible. Hopefully future studies will look more at the direct causality.

This is the start, once the association is made we first of all need to confirm that it can be repeated.

Once something is shown to be repeatable then we look at elaborating further.

You could try to do it all in one mega study but sadly funds, manpower and the complexity involved mean that it doesn't normally happen that way.