Torn page says nothing. Torn page can make Shiv suspicious or egg him to find things on his own. But I don't think it is sufficient enough for him to conclude he is not Ira's son!
Did Shiv meet the nurse himself or hear her talking about that stillborn female child thing? If not then how could he believe just Anandi?
Basant couldn't even believe his Maa sa's silence. Shiv believed a torn page and choo chaa of his wife?
I remember a similar track about Tulsi's son Harsh in Kyunki saas bhi kabhi bahu thi. The boy couldn't even believe Tulsi when she himself told him the truth that he wasn't her son.
Such huge things are hard to accept and believe even if one's own parents tell about it. And here Shiv was like "kaisa parivaar" over just what wife shared! What did he see himself? A mere torned page? This was enough for him to readily believe his family is not his own? Some attachment he has with Shekhars then!