I'll have to give in and say that if phonetics experts say that's the same sound, I'll have to rely on it. But that's one big problems for me in general - it describes qualitatively, not quantitatively, which makes everything rely on blurry statements and authority, not on empirical data like normal exact science.
There is no power of authority involved. Phonetics an phonology is a science, and as such, it is subject to peer review. The fact that you lack the skill or the tools doesn't make linguistic statements false. The fact that I have no idea which of the little twinkling things on the sky Venus, and that I do not own even a basic telescope, doesn't mean Venus is not there. Looking at various stars I see some are obviously bigger than others. Is it because they are loser? Brighter?
That you hear /k/ where /g/ is present is not unsurprising either. That's the interference you get from, ironically, basic education i.e. the skill of spelling. The word is spelled with a /k/ so you assume that this is what you hear and sometimes, as it became apparent, the illusion is hard to get over with. Somewhat similar phenomena occur with our visual faculties. I'm sure you know of many examples of visual illusion where you see a bent line, but the line is in fact straight and you can check it with a ruler. The ruler is a tool you know how to use. Linguistics, as you admit, is not among the tools at your disposal.
An example a little closer to linguistics, and specifically within the sphere of psycholinguistics, is one where a few words are misspelled, such as:
Cna yuo raed tihs?
The snetence is obviosly misspeld so it uses strings that do not exist in the English language, and yet understandable. Why? The answer is simple. It's our education. We have read these same words for a long, long time, over and over again. We no longer read words letter by letter. Instead we ended up learning their shapes. That is a sign we did well in our early yeas of education, but it also made us skip some of those misspelling when we proofread text written by ourselves. Words' shapes look fine so we miss the detail. That is also the reason why ALL CAPS ARE SO MUCH HARDER TO READ. THAT IS BECAUSE WE NEED TO CONCENTRATE MORE ON INDIVIDUAL LETTERS TO UNDERSTAND THE WORDS. Thatisalsothereasonwhyweincludespacesbetweenwordssowecandiscernindivid ualwordsmoreeasilly and why some German word, too many non-Germans, are so hard to read unless you spent a lot of time practicing.
To use the astronomical example above; good luck finding Venus on a clear night sky in Manhattan, NY. Too much light pollution (interference). People simply do not get to see the stars anymore. Which leads us to a little factual trivia.
When a few years ago the entire North East of the US and Canada went dark (massive power failures) emergency departments of larger cities in the affected area received a significant, number of calls. I heard about thousands of people who were reporting strange, lit objects on the sky. It turned out those were the stars. Both sad and funny, but for us here yet another example of how our experience sometimes throws us off in the way we perceive pictures, sounds, smells, touch (cold can feel hot) etc.
It's not hard to admit defeat as there's no battle in the first place, unless you treat a discussion as such, which tells more about you than anything else.
See? You're doing this again. Like you did when you put so much stress on who left Poland when, and whether someone knows a local jargon. That caused a blow back effect, as it turns out living in Poland doesn't ensure someone knows it all about the Polish language.
It'd make much sense in that even a book like "A Hundred Years of Solitude" could be analyzed quantitatively (statistically) if you knew what data could be useful for your goals and how to extract it.
This is a common misconception among those, for the lack of a better word, uninitiated. The popular view is that linguists just talks about talking. Some talk about how people should talk. That's prescriptive linguistics and I am far from being its fan. Punch Lyzo instead :) Anyway, linguistics encompasses may branches of science and art and it is is much larger than can be perceived by a casual observer.
Mathematics, logic and statistical analysis is in fact of curriculum in some linguistics departments. The courses may bear names not immediately associated with math (such as Computational Linguistics), but math is an essential tool used in those courses. Interestingly, linguistics is also used by mathematicians and computer scientists. Chomsky hierarchy was the basis for compiler construction and automata theory.
en.wikipedia.org/wiki/Chomsky_hierarchy
en.wikipedia.org/wiki/Automata_theory
So when you drop those few lines in the IDE of some compiler, wheather you're stuck with C++ or moved on to C# or Java, you are using the results of extensive linguistic research. Check the links just for kicks.
It's a fascinating area of study and I ad a chance to be exposed to it when I studied psychology. It was useful and I was getting my English Lit. degree and indispensable when I was taking compiler construction in Computer Science (incidentally, taught by a Pole, with a terrible English accent, from the University of Wroclaw).