Is boyfriend saying his is single to nosy people who tried to break us up okay?

Okay so a couple of months ago maybe more my boyfriend and I both wanted to post pictures of us on social media kinda of our way of tell people we are dating or more our friends and family but sadly on both of our parts since he wanted to rebuild his friendship with one of his ex girlfriend since they were long childhood friends so I told him that it's fine just as long as she doesn't get the wrong idea but things took a wrong turn three weeks after that and she thought he wanted her back so she and her best friend sent me messages on social media of how he was flirting and acting like his single but when it happened he told me that when they were talking she thought he wanted her back and he told her no and that he was already in a relationship with me. They ended up keep bugging me and telling me lies since I already had history with this girls best friend since we both went to school together and I knew already whatever she said to people were never true. In the end I ended up venting to someone who I thought was a friend but really wasn't since she tried to tell lies to me as well and help my boyfriend other ex out also who was also keeping tabs on me on social media but recently this same girl contacted my boyfriend and asked if we were still together in which my boyfriend said no were not together just so she wouldn't get nosy? Was that a good idea that my boyfriend did? Or was it a bad one? I mean through those couple of much it literally felt like my boyfriend and I were both dealing with high school drama all over again.
Is boyfriend saying his is single to nosy people who tried to break us up okay?
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