I assume it would be held in RAM maybe?
Yes, data acquired over the network has to be stored somewhere locally. It can be stored on hard disk for durability, but has at least to be somewhere in memory for usability. For very specific needs (sensitive operations) it can be made to be erased properly from memory immediately after use, or put in special parts of the memory that ensures only specific processes have access to it, and so on. But in your use case, the web, the content is displayed anyway at some point. So even if removed from memory, a screenshot just creates it again,
Not sure what REAL problem you are trying to solve (this really seems a typical X/Y case), but trying to think in term of "I am sending data to browser but the browser don't have any copy of it somehow" is not the correct way.