Thanks for poking at the formicary of philosophy -- the concepts of reality, existence, justification, truth, and belief.
My primary tool for dissolving questions is to ask "From what perspective?". From what perspective do the claims hold? From what perspective are the claims made?
The descriptions of both direct and indirect realism identify the concepts of an external reality and its interpretation by human senses and mind. Manfred in his comment provides some models from this perspective.
When I ask the question "From what perspective?", I see that these descriptions are from a third person perspective, a human perspective, and so these descriptions are from substantially the same context that that our first person experience of reality comes from. My answer to this question also came from a human perspective, and so is also from substantially the same context... and so forth in a seemingly pointless regression of justification.
From this it seems reasonable to claim that we have an anthropocentric perspective of reality, and every evaluation of our perspective on reality is also substantially anthropocentric.
(But you might say "We can build tools of math and science that provide perspectives that are independent of the human mind." To which I would respond that these tools were designed by humans, relate to reality as described from a human perspective, and produce results that are translated into the terms of human experience and understanding so that we can comprehend them.)
From this perspective neither direct nor indirect realism describe a universally objective situation, they are actually subjective anthropocentric descriptions. As such we should be able to identify contexts where these descriptions of realism are valid, are invalid, or are even meaningless.
What remains is a question of pragmatics, not of truth; is one of these perspectives on realism more useful than competing perspectives, for the context of current concern?
Stanford Encyclopedia : Perception
Wikipedia : Direct and Indirect Realism
On various philosophy forums I've participated on, there have been arguments between those who call themselves 'direct realists' and those who call themselves 'indirect realists'. The question is apparently about perception. Do we experience reality directly, or do we experience it indirectly?
When I was first initiated to the conversation, I immediately took the indirect side -- There is a ball, photons bounce off the ball, the frequency of those photons is changed by some properties of the ball, the photons hit my retina activating light-sensitive cells, those cells send signals to my brain communicating that they were activated, the signals make it to the visual cortex and...you know...some stuff happens, and I experience the sight of a ball.
So, my first thought in the conversation about Indirect vs Direct realism was that there was a lot of stuff in between the ball and my experience of it, so, it must be indirect.
But then I found that direct realists don't actually disagree about any part of that sequence of events I described above. For them as well, at least the few that have bothered to respond, photons bounce off a ball, interact with our retinas, send signals to the brain, etc. The physical process is apparently the same for both sides of the debate.
And when two sides vehemently disagree on something, and then when the question is broken down into easy, answerable questions you find that they actually agree on every relevant question, that tends to be a pretty good hint that it's a wrong question.
So, is this a wrong question? Is this just a debate about definitions? Is it a semantic argument, or is there a meaningful difference between Direct and Indirect Realism? In the paraphrased words of Eliezer, "Is there any way-the-world-could-be—any state of affairs—that corresponds to Direct Realism being true, or Indirect Realism being true?"