That is correct, and is a huge topic for discussion on the official forums, and have been for years.

Basically you play on the game shared server, but if you chose solo play, you are put into your own instance of the game, and can't see or interact with other players. You can however mess with some of the in game elements, like the political status of star systems (help rebel factions take over) Or affect the price of goods by trading massive bulk cargo, from system to system.

If there is a clan that is trying to take over a system, you can fuck with that clan in solo play, and they can't do shit about it, well other that out play you, like doing even more bulk trade for example.