As there is no benefit to having both in the search results, yours
gets suppressed. This is not a penalty. This is the algorithm doing its
job.
There are some content related manual actions, as covered in
Price’s article, but essentially copying one or two pages of someone
else’s content is not going to trigger them.
It is, however, potentially going to land you in other trouble if you
have no legal right to use that content. It also can detract from the
value your website brings to the user.
Verdict: SEO myth
HOW TO SPOT SEO MYTHS: 20 COMMON SEO MYTHS, DEBUNKED