Bjørn Kjos-Hanssen has answered the stated question but I think it would help to make a few clarifying comments.

Let BWQ denote the statement, "Every bounded infinite sequence from $\mathbb Q$ has an infinite Cauchy subsequence."  What Friedman has shown is <i>not</i> that BWQ implies Con(PA).  (I've gotten confused on this point myself in the past.)  Instead, what he has shown is that Con(RCA_0 + BWQ) implies Con(PA).  See Friedman's posts <a href="http://www.cs.nyu.edu/pipermail/fom/2015-May/018744.html">here</a> and <a href="http://www.cs.nyu.edu/pipermail/fom/2015-May/018752.html">here</a> for example.

If you're looking for other mundane-looking statements whose consistency implies the consistency of PA, then Simpson's book contains a number of candidates, e.g., 

1. Every countable field is isomorphic to a subfield of a countable algebraically closed field.
2. Every countable vector space over $\mathbb Q$ has a basis.
3. Every countable commutative ring has a maximal ideal.

Note: One has to be a bit careful about what exactly "countable objects" are in the context of subsystems of second-order arithmetic (as opposed to straight set theory); this fine print is discussed in Simpson's book.