When scripture quotes a non-biblical source, without any opposition of the source, does it imply any endorsement?

I think sometimes Protestants confuse the infallibility of the Bible with the Bible being the source of the Truth in describes. Truth is not Truth because its in the Bible. Truth is in the Bible because it is Truth. And just because something is not in the Bible doesn't make it not Truth. All humans have an inherent inkling of Truth "written on our hearts". We can still hold the Bible to be infallible without falling into the trap of exclusivity which tends to come across to others as snobbish arrogance. By acknowledging Truth where you find it, you build connections to people which can help them grow into a fuller understanding and acceptance of the fullness of Truth found in the Bible and Christianity.

The scripture records the thoughts of God and at times that includes referencing the opinions of men. When God refers to our thoughts it makes them no better, it only means God condescends to us through his word.

For those who believe that the words of scripture are actually chosen words of God, no writing can be compared to scripture. The Bible is a book all on its own that all other words, books and beliefs must bow under in revered submission.

Above all, you must understand that no prophecy of Scripture came about by the prophet’s own interpretation of things. For prophecy never had its origin in the human will, but prophets, though human, spoke from God as they were carried along by the Holy Spirit. (2 Peter 1:20-21, NIV)

Now everything in scripture is not necessarily treated as truth, even some of the lies and temptations of Satan are recorded in scripture. What the scripture does is treat all of the subjects that it treats, truthfully. It communicates in words, what the Spirit communicates to our hearts, God's mind. This makes scripture like a great valuable treasure above any other material wealth of this world.

Many books have truths in them. God gave us minds full of many truths. Even animals are born with innate truths within them. Yet when all these truths are written in all the libraries and data repositories, all of them combined are as a single penny compared to the unmeasurable weight of diamonds filling every word of scripture. As we properly estimate this immeasurable difference between scripture and any extra biblical work which it might use in its arguments, we would see that it is impossible to pass on any of its glory to them. When the scripture refers to the opinions of men, they are still 'mere opinions of men'.

I'm hesitant to give an across-the-board answer, but there is a well-established principle in understanding Scripture that applies somewhat here. It was included in an earlier answer of mine addressing the question of what we are to take literally as opposed to figuratively in Scripture, from a Fundamentalist standpoint.

First:

• [Because the Bible is inspired, it is inerrant, infallible, and authoritative][2]. No word of fallible man can stand in authority over Scripture.
  • Scripture is intelligible. God meant for us to understand it.
  • Because it is infallible, the Bible is internally consistent. it can't contradict itself.
  • Because God meant to communicate truth, and because Scripture is internally consistent, the words of Scripture have only one meaning in context. There may be multiple legitimate applications of a passage of Scripture, but a passage has only one meaning in context.

Then, the part that I think applies here, important bullet point bolded for emphasis:

Dr. David L. Cooper, the founder of The Biblical Research Society out it much more simply. Dr. Cooper is known for his “Golden Rule of Interpretation” which is as follows:

When the plain sense of Scripture makes common sense,seek no other sense;

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.

so, from this quote, from Dr. Cooper's perspective, we see that we are to take Scripture at face value (literally) unless...

• The immediate context makes it clear that the passage is not to be taken literally.
• Related passages, the literal sense does not make sense
• The literal sense of the passage would contradict axiomatic, fundamental truths.

That last principle can and should, from a Fundamentalist Sola Scriptura, Biblical inerrancy be applicable to anything questionable:

Does the passage contradict axiomatic, fundamental truths

If the Bible includes a passage, and doesn't oppose it in the context of the surrounding verses and doesn't contradict axiomatic, fundamental truths, then we can say, at best, that the author isn't opposing the statement, that it's not doctrinally incorrect, and that it's not blasphemous. I don't think we can go so far as to say Scripture (or the author of that particular passage) endorses the idea, unless it is clear, within the context of that passage that the author is endorsing it.