This was the rebuttal against the claim. And, it was so obvious to conservative speakers or old timers like me. I was actually baffled that people misunderstood this.

Also, If you are a native speaker, it is obvious (listen it first if you want https://www.youtube.com/watch?v=_UPIF2ql7pw ).

He says "Benim için mesela neler söylediler, çıktı bir tanesi aynı zihniyet Gürcüdür diyen oldu. Çıktı bir tanesi afedersin çok daha çirkin şeylerle Ermeni diyen oldu.." "then one another came out and told, excuse me, with much more uglier things, Armenian."

Grammatically you would not use the term "şeylerle - with..things" there to got the other meaning. Prosody and stops also would be weird to get that meaning. Use of "excuse me" before telling an inappropriate word is also very well known (not for a word like Armenian). It is common that in Turkey many politicians were smeared with slurs like "Armenian dölü-seed" or "Yunan dölü" and he was called with that. He is defining the adjective used frequently. Besides, he is known as the person who tries to break the ice with Armenians state level, do you think he would insult Armenians so calmly like that?

Your second link is based on a racist speech claim. However I cannot find the original Turkish speech to make more comments. But it is a well known fact that there is no black-white racism in Turkey. But please provide a better source to dig further.