For each main organization budget (i.e. EQ, RS, SS, Primary, YM & YW) only the presidency of that organization can submit requests (although they can submit the request to be paid to someone else). For certain other main categories (like Activities and Misc) the clerk can configure which organization can submit requests for those budgets. In addition, if the clerk creates a sub-category in a main organization category then they can give permission to other presidencies for the subcategory.
So if your wife needs reimbursement from the main RS budget then either she needs to submit the request (if she is a member of the RS presidency) or she needs to send it to a member of the presidency for them to submit.