Assuming the entities are not controlled, related, or affilliated, you are correct. However, when calulating the 1/2 of SE tax deduction for calculating earned income (for the sole proprietorship), the net SE gain (or loss) from unrelated entities has to be taken into account. If there is a net gain, the 1/2 of SE tax amount then has to be prorated (on some reasonable basis) between the two entities.
I've posted versions of
QP-SEP Illustrator Software in this forum; it may be usefull in crunching these numbers for you.
Link to QP-SEP Illustrator PostHope this helps.