Yes, that's correct. While the random cards you leave unspecified come indeed from the combined card pool of all participating players, the cards the host chooses need to come from what the host is subscribed to.
I assume it would make a much bigger problem if everybody could choose from all the cards, only to get an error message of "You need more cards that you are subscribed to" when they don't have another player at the table that has some subscription.
The solution would be that you are the table host and your friends tell you what cards they want. It might be cumbersome, but you can enter comma separated card lists in the kingdom selector, so if someone writes in chat
Please include Church, Moneylender, Wall
you can copy and paste "Church, Moneylender, Wall" into the kingdom selector and those cards will be included.