Well, related conspiracy theories are everywhere about Putin's ethnicity.
Apart from what you just mentioned, the ones who argue that he is Jewish, go with
1. Putin hasn't put anit-semitism as a state's policy - the first USSR - Russia leader since Lenin
2. Putin has been very suportive of Jewish issues during his presidency
3. his mother Maria Ivanovna Shelomova shares a similar surname as some Jewish surnames such as Shelomo and Shelomov; Putin was baptized into the Russian Orthodox faith at birth
4. His puppet Medvedev is likely Jewish
5. His nose shape ...
etc, etc...
However, I would go by the following logic:
1. For her mother's surname, Russian "shelom" шелом means курган, so Shelomova alone doesn't provide a clearcut proof. Baptization story lacks solid evidence as well.
2. We all know that Zionists control world media. World Media loved Boris Yetsin who, together with his Jewish Harvard friends/ International & Russian Jewish oligarchs, looted Russia to the last penny during privatisation era. On the contrary, it seems to me that world media dislike Putin. Times Megazien, NYT and Hollywood etc. (Jewish -controlled) repeatedly slanted Putin. This means something.
3. Zionist-controlled puppets dislike Putin: e.g. Jewish-controlled Obama doesn't like him, at all; during the latest US election campaign, McCain (Jewish-controlled) threateded to kick Russia out of G-8 ; Sarah Palin (a Jewish-controlled Nuclear-button admirer and nutter ) "can see Russia from her house"
... This all mean something.
4. Not all Russian oligarchs are Jewish, but int'l oligarchs mostly are. Yeltsin -era Int'l oligarchs operating in Russia got largely halted by Putin when he came into power.
5. KGB, where Putin came from, has been the bastion of anti-Semitism since 1930s to today. If Putin were Jewish, how could he has had survived there?
6. Russians in general are not fools. What the idiot Yetsin has brought down, Putin has put it up. Russia becomes much stronger under Putin than under Yelstin and Russians in general love Putin. This means something. Typical Jewish behaviours would be bringing down their host state to its knees. Hardly I can see that happending during Putin era.
7. Again, his nose, I've seen many Russians with the same shape of nose as Putin's.
Therefore, regardless conspiracy theories, by purely observing what actually Putin has been doing for Russia and Russians, I would say that Putin is not Jewish,
Whether Medvedev is or not isn't important.