Yes, you would need to do that to rule out the possibility. I understand your reluctance to do that, though as long as there's a router in the way and you're not browsing the web, it's not that dangerous.
I'm just throwing possibilities. I don't know how MC is coded, but I am a developer so I do know some possibilities. Nowadays it's normal for all kinds of apps to go online for a number of reasons, so this would not be so uncommon. MC is using some lib to decode FLAC; often these are 3rd party libs, not developed in house (again, I don't know if this is the case here). So it's possible that the lib itself has this functionality, and each time it's invoked to decode a file, it tries to do that.
MC itself downloads components/decoders as it needs them. So it's not unreasonable to think that it may check if there's a new version of the FLAC decoder each time this decoder is invoked.
I think you found a valid bug, and all this is just to try to find the root cause so that JRiver can fix it...