Conundrum: High pass filter passes DC?
The resolution to the conundrum is that there really is no conundrum.
Your input, a step function, has infinite dc component (its Laplace Transform, \$1/s\$, goes to infinity as \$s\rightarrow 0\$). Your output has a finite dc component. Therefore the transfer function of your filter, the ratio of the output to your input, has zero dc component because a finite number divided by infinity is zero. The transfer function has zero dc component, just as advertised.
If you put in any input with finite dc component, you will get zero dc component in your output. So, for example, as several comments have pointed out, if the input pulse steps back down to zero, you get the reverse spike that brings the dc component back to zero.