So I went into the log file and searched for the "Skipping update" line as the support team suggested. For my case, I was getting the "Skipping" a couple lines after a line that listed this as the problematic directory:
That's in your MATLAB/r2018a/ folder by the way.
I went into that directory and saw that there was a -OLD addition at the end of the .dll file. In other words, the file in that directory was named this:
I copied that file in the same directory and removed the -OLD from the end so that the file name ended with the .dll extension. I ran the update installer again and it worked!
Just for context, I was trying to update r2018a (update 1 I believe) to r2018a update 6.