Why does P/Poly can also receive bad advice?
Lets review the definition of the class $P/poly$ by Turing machines which take advice.

The class $T(n)/a(n)$ is the set of languages decidable by a Turing machine which runs in time $T(n)$ with advice of length $a(n)$.

More formally, $L\in T(n)/a(n)$ if there exists a Turing machine $M(x,y)$ and a sequence of strings $\left\{\alpha_n\right\}_{n\in\mathbb{N}}$, with $\alpha_n\in\left\{0,1\right\}^{a(n)}$, such that for all $x\in\left\{0,1\right\}^n$ $M$ runs in time $T(n)$ and $x\in L \iff M(x,\alpha_n)=1$. 

$P/Poly=\bigcup\limits_{c,d}n^c/n^d$. 

As you can see in the definition above, we only require the existence of some sequence of advice $\alpha_n$ that we can trust. Perhaps for some different sequence, $\beta_n\in\left\{0,1\right\}^{a(n)}$, and some $x\notin L$, it holds that $M(x,\beta_{|x|})=1$, but we don't care, since we only required the existence of a "good" sequence of advice.

This is unlike the case with $NP$, where if $x\notin L$, all witnesses must be rejected.