Now the script works, but I still don't understand!
I was advised to get the site and a page ad its _getActionUser('block') method. The but ran as BinBott and at _this point_ it asked for my sysop password. I wrote it. After this I ran my blocking script again, and it worked fine!!! But it didn't ask me for the password itself. I try to copy the relevant lines of my script here:
tag=u'Teszteszter'
user=userlib.User(site,tag)
if user.block(expiry='infinite', reason=blockmessage):
pywikibot.output(u'%s blokkolva van.' % user.name())
else:
pywikibot.output(u'%s blokkolása nem sikerült.' % user.name())

2010/10/23 <klaus.seiler@arcor.de>

If you are logged in as BinBot it wouldn't asked for the sysop password. Either log in as sysop or create a new directory and use one for the bot and one for sysop operations.

Greetings
xqt
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But my config has:
usernames['wikipedia']['hu'] = u'BinBott'
sysopnames['wikipedia']['hu'] = u'Bináris'
Once it is not logged in, it should ask for a password, shouldn't it?

--
Bináris