Another avenue for you to follow up on is that Jane's birth might have been illegitimate? There is one entry on IGI at
www.familysearch.org which is possibility:
JANE GRANT FENTY Birth: 25 FEB 1867 Turriff, Aberdeen, Scotland
Parents: Mother: JESSIE FENTY
If Jane knew the name of her father, it would not be unusual for her to include it in her marriage cert. What age do you have for Jane in her marriage cert in 1886? Also have you managed to find her in any census to give you an indication of where she was born (perhaps the 1891 census under her married name?).
If this turns out to be the right way to proceed, there is also a marriage of a Jessie Fenty which might be worthwhile following up on:
JESSIE FENTY Marriages: Spouse: GEORGE CASSIE
Marriage: 06 JUN 1868 King Edward, Aberdeen, Scotland
Regards.
Monica