convolution - A better explaination for 'there's no flipping of the impulse response'

I showed the question about flipping the impulse response to some math teachers and electrical engineers at an university. They read Dilip's answer and thought that it was hard to understand what Dilip meant and it was simply not true...

Could someone confirm that it really isn't true what Dilip Sarwate wrote. And explain it in a way that is easier to read.

See: Flipping the impulse response in convolution

There is no "flipping" of the impulse response by a linear (time-invariant) system. The output of a linear time-invariant system is the sum of scaled and time-delayed versions of the impulse response, not the "flipped" impulse response.