Did a Carnival Baltic cruise in 2013 from Dover and quite a few UK and US passengers were told they had to stay on the ship in the St Pete's port as they had no tours and visas.

One could take from that they were definitely allowed to board without Russian visas.

For those of you on private tours and ship ones the reason you didn't need a Visa is because it was included in your tour. Most nations need a visa in Russia- I can't remember which countries are exempt.
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Norway 10 day on the Norwegian Jade August 2017
Mediterranean 12 day on Carnival Vista August 2016
Atlantic Coast 7 day on the Royal Caribbean Independence of the seas May 2016
Mediterranean 13 day on the Celebrity Equinox August 2015
Panama Canal and Caribbean 13 day on the Carnival Legend August 2014
Baltic 12 day on the Carnival Legend August 2013