Question about Mapping Reductions (Clarify Example) I cannot for the life of me wrap my head around these reductions.

Specifically, the example I'm wrestling with:

REGULAR = {&lt;M&gt; | M is a Turing Machine and L(M) is regular}

Reduction to ACCEPT_TM where ACCEPT_TM = {&lt;M,w&gt; | M is a TM and w is a string, M accepts w}

Construct TM M':
M' = "On input x
    1. If x has the form 0^n1^n, accept
    2. Otherwise, run M on input w and accept if M accepts w."


If M accepts w, M' accepts SIGMA*
If M does not accept w, M' accepts 0^n1^n


I understand the first implication (if M accepts w, M' accepts SIGMA*).

What I don't understand is the implication that if M does not accept w, then M' accepts strings of the form 0^n1^n.  How are they reaching this conclusion?  To me, it seems like "If x is in the form 0^n1^n, then don't run M", which doesn't seem logically equivalent.
If M does not accept w, then the only case in which M' accepts is if its input is of the form 0^n 1^n.