Well if that were the case it would be perfectly pointless to make such a visualization... The goal of dimensionality reduction is to provide a useful summarization of the data; it is a valid question to ask to what degree it is successful at that.
From the guy who helped make t-sne:
When I run t-SNE, I get a strange ‘ball’ with uniformly distributed points?
This usually indicates you set your perplexity way too high. All points now want to be equidistant. The result you got is the closest you can get to equidistant points as is possible in two dimensions. If lowering the perplexity doesn’t help, you might have run into the problem described in the next question. Similar effects may also occur when you use highly non-metric similarities as input.