Nope. I'm afraid you're wrong on this. I am a very sad individual and the Group Stage draw day is my Christmas Day - I have spreadsheets based on which airlines fly to the various airports closest to each team which qualifies. It's taken a while but I have learned how the draw works, and it isn't fixed - but weighted towards certain probabilities. Thankfully the probabilities have changed a bit this year.
For the ease of explanation I'll use the example of Barca and Real. As Barca are in Pot 1, lets say they get picked out first. They can be placed in any group A-H, lets say they get put in Pot C. All the other Pot 1 teams are drawn out and can be placed anywhere (with the exception of Chelsea this year, but too complicated to explain why on here without various diagrams). Then Pot 2 will be drawn. Real Madrid can only be placed in groups E F G or H. If you can find me an example in the last 5 years (probably longer) where Real and Barca have been in the same half (the halves are A-D and E-H) I will pay for you to go on a European trip next year.