Well first of all, no one who paid attention in class adopts this strawman caricature view of the educated approach to the world.
Case in point - I spent a good part of my academic career studying pure mathematics. Which deals exclusively with abstract entities, about which the physical sciences provide no input. Instead, pure mathematics involves applying well-defined formal rules of inference to well-defined axioms about those abstract entities. One might try to claim that the formulation of a mathematical proof constitutes an “observation” about those entities, but this is stretching the definition of “observation”, possibly beyond reasonable limits, though the relevant philosophers will almost certainly build careers arguing about this idea.
Likewise, those of us who paid attention in class, recognise the value of philosophy, when it is conducted properly. The purpose of philosophy isn’t to answer questions, but to determine which questions are pertinent to ask. That philosophy has an unfortunate habit of being hijacked by assertionists (and indeed lends itself to such hijacking with dangerous ease) doesn’t detract from this, it merely requires us to be vigilant with respect to keeping assertionist cant at bay.
So, I’ve already provided two examples of methods of acquiring knowledge that are, in their own realms, reliable, and recognised as such by those of us who paid attention in class.
However, with respect to concrete entities, the scientific method is not only demonstrably reliable, but has no real competition. Observing how concrete entities behave, and deducing relevant relationships inherent thereto, has been, to use the words of one biographer of Nietzsche, “terrifyingly successful”. Those who wish to assert otherwise have a lot of work ahead of them. Namely:
[1] Demonstrate that you have an alternative methodology, whose components and operation are well-defined in detail;
[2] Demonstrate that your alternative methodology sorts relevant propositions into “true” and “false” categories in a testably reliable manner;
[3] Demonstrate that your alternative methodology is applicable to concrete entities.
Without the above steps, all you have is hot air.