Shareholders with voting shares have the right to attend shareholders meetings and vote in the board of directors. In such large corporations, shareholders usually appoint a proxyholder who attends the meeting and votes on the shareholder's behalf.
My understanding was that Nokia Plan B was basically soliciting such proxies by asking shareholders to give their votes to them for the purpose of replacing the board.
Corporate law usually doesn't require a proxyholder to be a shareholder, so they actually didn't even need such a (weak) claim to authority.
As a side note, soliciting proxies usually requires following proper corporate law procedure by sending prescribed materials. Nokia Plan B just had a website, which was an early indication this was a fake.