I think it is perfectly acceptable to take offense at the incorrect, anachronistic pronunciation of a supposed teacher of Ancient Greek. Teachers have a duty to know their subject well and to accurately convey that knowledge to students. It seems that the current scholarly consensus on the pronunciation of Attic was settled some decades ago, so there is no excuse for a professional teacher to lack this knowledge. Nonetheless, I wonder if, when teaching students whose native tongue is Modern Greek, pronouncing the ancient language in the modern fashion makes the ancient literature feel more familiar, and perhaps even understandable, to young students who have not yet learned to decipher the older varieties of their language. If this is the case, then it is acceptable for a teacher to read texts to such students in this fashion, as a way to engage them, as long as the teacher makes it clear that the ancient language sounded quite different. Furthermore, the teacher should also recite the old Greek in its re-created native accent, so that the students understand the aural component, as we currently understand it, of the literary art of these venerated works.
I also found samples of the re-created accent of Attic to be quite ridiculous, and the rules that shape them ridiculously difficult to comprehend, when I first discovered them. But then again, when I first learned Spanish as a youngster, its pure vowels and the machine-gun like persistence of its syllables sounded ridiculous to my North American ears, and I felt "fake" when I tried to mimic its accent properly. As I continued learning and practicing, as well as conversing with native speakers, my ear for Spanish developed. I learned to appreciate its unique soundworld and to enter it at will. I found myself being struck with a flash of recognition of the beauty of the language when hearing the variety of forms of its literary art, from poetry to cinematic dialogue to creative cursing. Now my former childish bias seems quite silly, but that doesn't mean I've been cured of it. More recently, I've been learning Russian, and its soft consonants, vowel reductions, preposterous combinations of consonants and unheard of sounds such as the vowel ы, have been driving me crazy. Each language has its own soundworld that presents unique aesthetic and, in combination with its grammar and syntax, semantic opportunities. Pitch accents, as scholars understand their use in the ancient Greek and other ancient Indo-European languages, are going to sound very foreign to speakers of many, if not all, modern languages. Just because it is unfamiliar does not mean that it is ridiculous.
While it is true that we cannot know exactly how the ancient varieties of Greek sounded, that any re-creations of their sound are by definition artificial and that some new scholarly method or discovery may yet add new layers to our current understanding of their pronunciation, careful scholarship can make us nearly certain of many things, approximate in others and clear about what we do not know. The current consensus is based on well-documented analysis that one can follow if one has doubts about the conclusions that have been reached. This consensus also elucidates the craft of ancient authors within the forms of their literary work to which we now have access. Perhaps we are unable to thoroughly re-create the sound of these works as their authors and original audiences heard them, but it has been demonstrated that we can, by following the scholarly models, imitate most of what the ancients heard. One can be forgiven for not being able to perform perfectly a work composed in a foreign language, especially when one has no native models to follow. One should feel free to enjoy any literature in translation or to appreciate an historical language as a collection of morphemes that have, in much altered form, had a great impact on contemporary languages as well as contemporary life and thought. One may even recite ancient literature in what is known to be an incorrect fashion, to quote it, to cut and paste it, to add music to it, to make something new out of it (the performance posted by one of the commenters above, for example, uses a Modern Greek pronunciation, and I find its performance as a new work of music to be aesthetically pleasing). But to knowingly disregard the pronunciation that is correct as far as we know and to simultaneously claim that you are reciting Ancient Greek, that is dishonest, damaging to any attempt at an appreciation of these works in their original contexts and worthy of offense.