Intertextuality as you have observed is a secular principle, which could be applied to a wide range of texts and settings. It is basically a way of explicitly describing that there is an expected interrelationship between texts. Normally in hermeneutics we prize 'exegesis', reading meaning out of the text at hand, and that's our typical focus here on BH.SE.
Scripture interprets scripture is a theistic principle, where the literary intent is suggested to be such that a text should be read in light of other surrounding texts. There is a fluffy interrelationship between this concept and other theological concepts like the inspiration of Biblical texts, or further down the spectrum ideas like inerrancy.
People handle these concepts differently
Ultimately the process of exegesis usually takes us away from these kinds of concepts - i.e. we try to avoid injecting modern concepts and principles into texts before deriving their meaning. However, there are a range of hermeneutical approaches (past and present), and there's no getting away from the fact that each of our approaches to passages will hinge on our attitude towards these theological principles.
The closer a question gets towards mandating one or more theological principles ahead of interpreting the passage, the more likely it is to be off-topic here. It's okay for individual users to supply answers that agree with a variety of theological stances on any issue (including the Trinity, inerrancy and others), but generally Questions shouldn't force users to go down one route or another - they should be focused on the text in its own intended context.
In essence, intertextuality is a valid exegetical principle, because it affirms that there is some sort of clear and valid link between the texts in front of us.
Examples
As one good example, Soldarnal once asked a good question about whether a passage in John is intended to evoke a passage in Leviticus.
Similarly, Michael once asked a question about an intended link between John and Ecclesiastes. This is anchoring back on the core hermeneutical principle of authorial intent - what did the author mean by what they said?
This question about Psalm 149 doesn't seem to quite apply it correctly:
Psalm 149 was written a long time before Romans, and so it's incorrect to ask what the author meant as if they had Romans in front of them at the moment when they wrote it. Though on examination, Romans is actually quoting from Deuteronomy 32:35, so perhaps the reference just needs to be adjusted.
Conclusion
Essentially the two principles are similar, but distinct. A question on intertextuality implies a link between passages that may/should affect the process of interpretation, whereas scripture interprets scripture affirms that one of the texts was intended by the author to be read in light of the other. So it's carrying an extra assumption into the text, if that helps disambiguate the concepts.
So, no - intertextuality is a fair and general hermeneutical tool, and doesn't risk or necessitate carrying theological baggage into the passage.
