Was I wrong to reach out to my daughters ex?

My daughter is 21 and my grandson is 2 months old. My daughter and her ex boyfriend has broken up and when she told him she was pregnant she told me he blocked her. He had told people that's not why he blocked her. That my daughter was crazy and she cheated on him. I did take things to social media and called him out for lying and ghosting my daughter while she's pregnant and HIS mom got involved and told me to keep her son's name out of my mouth and until there's a DNA test he wants nothing to do with her. There was a lot of back and forth my daughter's whole pregnancy and we had our court date and they said that he was not the father. My daughter was clearly humiliated. I was shocked because I genuinely believed everything she told me. I decided to reach out and just say I'm sorry I put him through so much and wished him well. He replied that it was cool. My daughter found out I messaged him and is mad at me because she thought I was on her side. I didn't see it about being on a side. I talked a lot of shit and was wrong and borderline harassed this guy because I thought he was painting my daughter as a cheater and trying to avoid responsibility.