A search of Minnesota birth certificate index lists no Thomas Miller Fenton or any variation of the name. Link: http://people.mnhs.org/bci/search.cfm
I have been searching off and on since your posting but have found nothing. I'm inclined to agree with your statement of: "I'm starting to suspect she may not have been completely honest!"
I find it strange that an exact date is known for his birth and marriage but not his death. Maybe they were never married and he never died but just left her or she may have left him. Just my thoughts.