Hello :)
That is her husband; I do not know why he is marked as single, but all his other information is correct, and I've matched the ship manifest with what he stated on his naturalization paperwork. I obtained his sister's Social Security application, and their father's name was Tomasz Tanecznik, which appears to match the ship manifest from his arrival.
When Jennie and son Karl arrived in 1908 (leaving baby Emma, b. Feb 1907, presumably in Bohemia - she came to the U.S. in her mid teens) that ship manifest said they were joining Michael Tanecznik, husband/father. I do not know when or where they married, or even how they would have met - their hometowns were not near each other. I don't know whether either of them spoke any English before they arrived, but on the 1910 U.S. Census it says they both spoke Polish.
Cerhovice is listed as Jennie Wild Tanecznik's birthplace on the ship manifest from her arrival. Her last residence is listed as Burenice, and her mother's name appears to be Maria Muka. However I did just receive her (1972) Social Security application yesterday, and she listed her parents as Mary Rudolph (Rudolph is apparently the surname of Mary's stepfather), and Frank Wild.
I will also be requesting Michael's SS-5, to ensure it matches what is written on his sister's. He did not show up in the SSDI on Ancestry, so I assumed he didn't have a SSN. However, the letter from SSA that I received with Jennie's information provided his SSN as well, since she originally applied for benefits under it.