The paper "Pin cobordism and related topics" http://retro.seals.ch/cntmng?pid=comahe-002:1969:44::42. only gives the homotopy groups of 
$RP^{\infty }\wedge X$ where $X$ is either $\Sigma ^nHZ/2$, $bo\langle 8n\rangle$ and
$bo\langle 8n+2\rangle$, noting that they are summands of the homotopy groups of the spectrum
$MPin$.  However, it doesn't say how many copies of them actually show up.  To find it out, you have to refer to the paper <a href="http://www.jstor.org/discover/10.2307/1970690?uid=3738016&uid=2481646813&uid=2129&uid=2&uid=70&uid=3&uid=60&sid=21104367554033">"Structure of Spin Cobordism Ring"</a> by the same authors, Theorem 2.2 (and the definition of $J$'s on the top of the same page).  

Thus
$RP^{\infty }\wedge bo\langle 8n\rangle$ appears as many times as the number of the sequences $(j_1,\cdot j_k)$, $j_i\geq 1$, $k\geq 0$ ($k=0$ means
that we have an empty sequence) with $j_1+\cdot +j_k=2n$

and $RP^{\infty }\wedge bo\langle 8n-2\rangle$ appears  as many times as the number of the sequences $(j_1,\cdot j_k)$, $j_i\geq 1$, $k\geq 0$ ($k=0$ means
that we have an empty sequence) with $j_1+\cdot +j_k=2n+1$

For the latter here is no such sequence when $n=0$, this is why there is no contribution of $bo\langle -2\rangle$.

As to the case of dimension 22 there will be one copy of $bo\langle 0\rangle$,
one copy of $bo\langle 8\rangle$ and two copies of $bo\langle 16\rangle$ 
(one for the sequence $ (2,2)$ and another for $(4)$) as well as a copy of
$bo\langle 10\rangle$ and two copies of $bo\langle 18\rangle$.  Thus there is no contradiction.