How could it be that phoneticians differ so sharply from lay native speakers in their ability to perceive this distinction in German? Given all that has been described so far about probabilistic perceptual outputs and about how response choices are affected both by stimulus analysis as well as other criteria, the answer is quite simple. They performed completely different tasks. Phoneticians and linguists are professionally concerned with establishing and applying consistently a set of phonetic units that are plausible candidates for `the universal phonetic space'. They would be understandably reluctant to claim to have discovered some categorical difference that they can only differentiate with, say 70% accuracy. That is, given the standard theory of phonetics, there are many criteria aside from the mere perceptibility of a difference that are relevant to their decisions about what phonetic transcription to use. We might say that they have a professionally motivated response bias. Only differences that are large enough and reliable enough are of interest. Thus it is important for them to ignore mere token-to-token variation, speaker idiosyncrasies, minor dialect differences, and so forth. Very likely these phoneticians and phonologists agree with C-H that any distinction that is to be represented in the universal phonetic alphabet must be large enough that it might be useful (in some imaginable situation) within a language to distinguish words with fair reliability. From the perspective of these criteria, there is no question that the two [t]s in Bund and bunt should not be differentiated. They are indeed too similar to be of contrastive use.
On the other hand, in our discrimination experiments with native speaking Germans, the question we asked them was ``Which word did the speaker say?'' - rather than ``Which phonetic symbols would you use to describe these sounds?'' So these listeners used all the acoustic evidence they could find to make their guess. There is no question in my mind that any serious phonetician, whether or not a native speaker of German, could do nearly as well as our German listeners at the word identity task with very small amount of training with feedback (eg, 10-20 trials). I am not a fluent speaker of German but was able myself to perform as well at the task as our better German listeners. Like our subjects, I knew that there was an equal number of underlying /d/s and /t/s, so I just listened for more D-like vs. less D-like stimuli. The point is that choosing a phonetic transcription and identifying a word are two vastly different tasks with little in common except the stimuli themselves. It is little wonder that the phoneticians ignored these minute differences in assigning their transcription, but neither is it surprising that the native listeners did use this information in identifying the words.
The view within traditional phonology that phonetic transcriptions can be reliably and discretely assigned is a bit naive, it seems to me. What seems to be happening in the field is that the discipline of phonology is in the process of splitting between those who do careful experimental studies of speech and those who insist that impressionistic phonetics, often obtained largely from secondary sources, is good enough.