Published in the Eugene Guard, 27 Dec 1913, page 3, column 7: Born to Mr. & Mrs. M.L. SMITH of 245 Madison, on 23 December 1913, a daughter.
The Lane county birth records say: SMITH, Vera Nelley (or Nellay), born 23 Dec 1913 in Eugene.Father: Melvin L. SMITH, age 22, salesman. Mother: Mabel Marie KLOSTER, age 18, housewife.
I don't find this SMITH family in the 1912 or 1918 Eugene city directories.
I don't find a marriage record for this couple in the Lane county records at all, or in the Oregon State marriage index from 1906 to 1915.
There weren't very many births in Lane county at that time.(I estimate roughly 2 female babies every 3 days.)It seems too great a coincidence that there should be another daughter Vera with mother Mabel on exactly that date who is not your grandmother.
On the other hand, both the newspaper coverage and the county birth records for that time are very spotty, so it's certainly possible that there was another birth that went unrecorded in both of those places.
I think the question is whether Melvin L. SMITH is S. LESNEWSKY by another name or a different man entirely.