The phrase "rightly assume" is correct and usable in written English.
You can use it to mean that something is assumed to be valid or true based on the available facts. For example, you might say, "We can rightly assume that the proposal will receive enthusiastic support from the senior management team."
We rightly assume that what they publish is what they intend.
No one could rightly assume that this sudden emergence of Buddy Roemer out of nowhere could now be stopped.
They will rightly assume means that the works are from the collection of Jacques Koerfer, the German-born collector and former chairman of BMW, who died in 1991.
When we hear the words 'rehabilitation' and 'green zone', we immediately think of Iraq and rightly assume it to be ironic.
The Taliban has refused to engage with the current government, as they rightly assume that the incoming administration will have different policies from its predecessor.
But if, year in and year out, a teacher's students consistently under- or overperform with respect to predictions, one can rightly assume that some significant proportion of student performance is the result of that teacher.
The composer, quite rightly, assumed that the problem lay with the book and libretto, not the music.
He rightly assumed that this created excitement in the audience, but all musical thought had to stop until the process had subsided.
When my wife's mum first visited us in London, she rightly assumed we'd be bereft of one, and so she brought this.
Companies, it was rightly assumed, were tiny fascist states in which the workers were meant to feel lucky to have citizenship.
And then, when George [Lucas] said that they wanted to do more, I rightly assumed that it wouldn't be our story, because we had a beginning, a middle and an end.
