Thank you, Raysusher.
OK, this is starting to look like a corporate firewall issue. I uninstalled VLC, then went to their website for the download. At first I couldn't get through due to a certificate error. After a few retries, I got through to a pure white page with text only, no cone logo, no images. I found the download link, took the file and verified it against what I already had. I'm now running that newly downloaded VLC, and the video caption problem persists. However the apparent 'naked' VLC website makes me suspicious things are getting blocked on my employer's end. The video in question could still be bad, but streaming might be getting interfered with.
This is the website I was looking at.
Episodes 1-12 in AVI format are perfect.
Episodes 13-onward in MKV format all display the caption problem. Music lyrics are perfect, Dialog text is that "flower" clump i mentioned.