I really do feel that Gilliard has been misquoted by AA supporters over the years, such as the hairdo quote. There is no way he's going to accuse AA of copying AN's hairstyle in Tobolsk when AA's hair was very long and twisted up in a bun, and AN had been shaved totally bald after the March revolution due to measles and her hair was short for the rest of her life. Gilliard himself took the bald pics of the GDs so he knew better. It would be to the advantage of AA supporters to discredit him, since he was one of the main opponents and had known AN so well. Poor Ernie was dead and Olga continued to be accused of lying all her life. What happens to the guy in the movie who 'knew too much?' He's rubbed out, right? Well, if you can't rub someone out physically, the next best thing is to set out to destroy their credibility so no one will believe anything they say. I've seen this happen in real life, sadly.
IF he DID make proven false statements in his own book, there are two possibilities- one, he just plain remembered wrong, as I suspect was the case in many of the 'hesaidshesaid' pro AA comments about shoes, height, etc. It happens to the best of people. Also, it is possible, I suppose, that he said things to help boost the case against her that weren't true, though he knew she really wasn't AN, he wanted to add more to his side. This is not good, as it hurts your case in the long run. It's like the LAPD in the OJ case, they knew he did it, but in trying to make sure he was found guilty, they shot themselves in the foot and left suspicion that helped get him off. But that doesn't mean OJ is innocent,and AA was certainly not AN.