What is the basis for such an office called by the session but not the congregation?
It is still "the church" that issues the call. Other examples include missionaries and military chaplains (and I suppose other chaplains) and seminary professors. These men,
if they will be ordained, must be acknowledged as having been called by the church to the jobs they are set to perform. Some men do some of those jobs without ordination.
But, what church body processes the call? In my experience, it is always or almost always the Presbytery, that is to say: the governing body of the regional church. Presbyterys typically end up issuing calls to seminary professors and chaplains. In like manner to the session, acting as the church (as does a presbytery or general assembly--which in the OPC through its committee on foreign missions calls a missionary) issues a call to a man to be an assistant pastor. That call must still be processed by some Presbytery, which will be the body that ordains (if the man is not yet ordained) and then to which the minister is accountable.
I speak out of the experience of being called for the first time by a PCA session, having been until then only in the OPC which does not employ "assistant pastors" in its polity. I don't recall how much reflection I did on the matter immediately upon receiving the call. Being trained by PCA professors (mostly) at GPTS, I had some indirect prior familiarity with the position of "assistant pastor," and the justification for it.
I knew of some "assistant pastors" in some large PCA churches who were
not ordained; that is, they held the position through title, not through actual ordination. These men truly were "staff," possibly in positions like "youth pastor." The men who were ordained would, like myself later on, be ordained by Presbytery in taking an actual call from a church-body, viz. the session of a church.
However, my call, like calls to seminary professors and others, did not result in sessional authority. Men like myself worked
for the session, not
on the session. Similarly, missionaries called by GA are not automatic commissioners to GA, though they work for the church in denominational roles bearing ordained office. The only congregational authority I possessed was indirect. It was the result of whatever demonstration of biblical instruction and benefit I might exhibit. Just as the body would receive a visiting pastor's preaching as authoritative based on his ordination and their session allowing him in the pulpit, just so much was the authority I had.
Inasmuch as my gifts were well-received, I felt able to serve the people of that congregation, even though I did not have any direct power over any. I sat in no judgment seat. I attended session meetings, but did no voting on any matter. When the time came for a transition of senior pastor, in his absence I presided (moderated) session meetings, though I did no voting then either. As the congregation sought replacement for their senior pastor with someone of greater experience than I had, I prepared for departure from that assistant pastor position. My next call was to a position of "pastor" (solo) in another congregation.
I have seen recently doubts raised from some quarter about whether the church should call men to positions like seminary professor; thereby calling into question the position of assistant pastor. Possibly, the original objection was to "assistant pastor;" but seeing that such a call and ordination rests on the prior acceptance of such extra-congregational calls as "seminary professor," it follows that one must object to the whole range of calls issued by bodies other than congregations. If seminary professors would then be ordained, then first they must be called by a congregation.
