No. The French motion should not stipulate “un membre du personnel ou de son parti”, but rather “un membre du personnel de son parti”. There should not have to be any mention of whether or not the staff person is from the MP's office, because a person who works for an MP also works for the party as a whole.
The motion, drafted in French, should read as follows: “[...] each committee member be allowed to be accompanied by a staff member of his party at an in-camera meeting”.
For example, someone from the research bureau should be allowed to accompany me. That person is not necessarily someone who works directly for me in my office.