Is the diode in this circuit connected in parallel with the resistor?
What we say isn't always precisely what we mean.

I think he meant to say 'the diode is connected in parallel with the signal at Vout'. 

In this case, the signal Vin is generated by the AC source, and goes through a resistance R, before being read at the + and - terminals of Vout.

The diode/battery combination is in parallel to the signal at Vout.

There is an alternative clipping circuit, a series clipper, where the diode would be in series with the R, being placed in the line between R and Vout+.

Having said that it's a parallel clipper, it's 'obvious' to your teacher and any engineer that the diode is in parallel to Vout, and in parallel to where the resistor R connects to Vout. This is probably the source of his momentary lapse in precision. Of course, it's not obvious to somebody learning.