I can tell you that the German authorities are allowed to request financial proof of foreigners who want to live in Germany. This is not something that only the German authorities do, but is the standard procedure in every EU country whenever foreigners apply for residence.
This is governed by the EU Directive 2004/38/EC on the right of EU citizens and their family to freely move and reside in another country. You can find the Directive in full here:
http://eur-lex.europa.eu/LexUriServ/Lex ... 123:en:PDF
According to Art. 7, the right to settle down in another EU country is conditional on either being (self-)employed or at least having sufficient personal financial means so that you do not have to rely on the welfare benefits of the host country. This is a mere formality, though. You can, for example, provide a balance sheet of your bank account. Also, the German government has clarified that the threshold is very low: all that
you need is a personal income that exceeds the minimum social welfare benefit in Germany so that you can support yourselves from your savings.
This compulsory income check never applies to EU foreigners who already have a job or are self-employed.