Hey Ryan B, how are you? I hope you are doing just fine!
As Greg said, the expression ''harden into'' means the same as ''make or become more resolute, certain or set in(to) something.'' Another meaning could also be ''to make or become fixed/settled in(to) something''. As regards the context that you provided, the idea conveyed is that the untruth or even something that is nearly true, which is usually begotten by some sort of misunderstanding, is so likely to spread across a huge number of people that it is soon considered or taken to be the absolute truth.
The usage of ''in(to)'' after ''harden'' is considered necessary to the context as it reveals in which condition/state, form or result ''something'' is being settled or fixed.
Below you shall find a set of other useful examples:
1) ''Let these lies be hardened into the truth.''
2) ''Your statements have hardened into yet another scandal.''
3) ''I believe his ideas will harden into a great endeavour for mankind.''
4) ''Mom says Jon's behaviour is hardening into that of an aggressive man.''
Hope that helps!
Should you have any further questions, do not hesitate to contact me. I shall be pleased to help.