Unless I'm mistaken, there is absolutely no way to "prove" with complete certainty what is being rendered on a client's machine, since they could be running any number of scripts client-side that might change or alter what they're actually seeing. You can't "prove" that an unknown user isn't running the Chuck Norris Picture Replacement plugin on Chrome, for example (yes, that's a real thing). They could literally be seeing anything.
And here, I intend to use the word "prove" in the strict sense, not necessarily in the legal sense. To prove something legally in a civil case, you need only a preponderance of the evidence (i.e., anything that would make it more than 50% likely that it's true). So if you can show that it's more likely than not that they saw the picture (as it's unlikely they're using the Chuck Norris Picture Replacement plugin, for example), then you have "proven" that they saw the image as far as you would need to for legal purposes. (I happen to be a lawyer in addition to a web developer, if that generates any additional confidence in the answer I provided).