I simply limit myself to saying something like:

• You know what... the other day I saw a documentary...
• I think I once read an article/news/book that said...
• I saw a video about that on YouTube the other day, and it was really interesting because it said...

If I'm feeling confident enough, I'll say something like:

• I think I have a different opinion on the subject... if you give me 5 minutes, can we watch it?
• I studied the subject a while ago, and I had a different point of view. It turns out...