Hold off refinancing. Rates are projected to drop again next week.
(A little insider info since I work in the banking industry).
They're right - there are no out of pocket costs. She'll roll the closing costs of the refi into the mortgage. If your home hasn't gone up in value much (not uncommon in today'* economy) and you haven't paid down on the existing principal, then you'll likely find that the home will not appraise for enough to cover what you need to borrow PLUS the rolled in closing costs.
And, getting a new appraisal due to a refinance will not increase or decrease your taxes. Your taxes are levied differently after the property is owned. A change of ownership will reset the SEV and appraised value. Not a refinance.