Issue with parallel resistors in LTSpice
I tried to replicate, and I saw the same behavior. @SteveG did, too. After a few questions regarding the sanity of each of us, I think I found why, and it is pretty simple:

Are you absolutely sure you are actually plotting the right voltage node? In both of your plots, it shows "V(n003)/I(V1)". But I actually realized that if I mess up just a bit with the schematics, the node names change. In my case, n003 became n001 when I added the resistors, or just changed the wires layout.

To overcome this, you can explicitly name your nets by putting labels.