Using the basic rules that Biblical Literalists use when determining what is to be taken as "literally the Word of God", we find the basic principle:
When the plain sense of Scripture makes common sense,seek no other
Therefore, take every word at its primary, ordinary, usual, literal
meaning unless the facts of the immediate context, studied in the
light of related passages and axiomatic and fundamental truths
indicate clearly otherwise.
That makes things pretty simple. In context, this was an Epistle, which is to day, a letter of instruction to the Church at Corinth. Literally, Paul is saying that this is something he is speaking "with permission" - that is, the author himself is stating that this is his personal position, not something that the Holy Spirit guided him to write.
Therefore, it is reasonable to believe and understand that these words were not laid upon Paul by the Holy Spirit, but "by permission" indicates that he had the Holy Spirit's permission to write these things. That implies he sought out the will of God in these things and found no opposition or reason not to write these things.
This means, logically, that these verses are not the direct inspiration of the Holy Spirit, but are not in contradiction to the will of God.
This is all in line with the Jamieson-Fausset-Brown Bible Commentary
- no commandment of the Lord: yet . my judgment-I have no express revelation from the Lord commanding it, but I give my judgment
(opinion); namely, under the ordinary inspiration which accompanied
the apostles in all their canonical writings (compare 1Co 7:40; 1Co
14:37; 1Th 4:15). The Lord inspires me in this case to give you only a
recommendation, which you are free to adopt or reject-not a positive
command. In the second case (1Co 7:10, 11) it was a positive command;
for the Lord had already made known His will (Mal 2:14, 15; Mt 5:31,
32). In the third case (1Co 7:12), the Old Testament commandment of
God to put away strange wives (Ezr 10:3), Paul by the Spirit revokes.
Then again, Clarke's commentary states:
I have no commandment of the Lord - There is nothing in the sacred
writings that directly touches this point.
Yet I give my judgment - As every way equal to such commandments had
there been any, seeing I have received the teaching of his own Spirit,
and have obtained mercy of the Lord to be faithful to this heavenly
gift, so that it abides with me to lead me into all truth. In this way
I think the apostle's words may be safely understood.
Which, of course, would indicate that this is the direct inspiration of the Holy Spirit, which leaves the concept of a fully inspired Scripture intact.
So apparently the answer to the question is, not surprisingly, "There seems to be more than one point of view on the subject, neither authoritative."
As a sige point, this isn't the only place in 1 Corinthians where such a statement is made. Verse 6 has a similar statement (KJV):
But I speak this by permission, and not of commandment.
which most commentaries interpret to be referring to the preceding verse, but again, interpret differently.