This all sounds much more ideological to me than the comment to which you are objecting.
It is true that people will often use it as a lazy and fallacious way of vilifying but please note this is not exclusively a progressive phenomenon. Many of these groups lobby for things like govt subsidies, laws which restrict personal freedoms in ways that help their industry, etc...many conservatives aren't thrilled with such behavior.
In a brief non scientific survey of a few subreddits (r/libertarian, r/socialism, etc) phrases like "big oil" appear roughly comparably.
People on both ends of the political spectrum are (perhaps rightly) displeased with some of the actions of such groups and vilify them - they just disagree about what the root cause is and how to prevent such behavior.
The fallacy comes in when people use some particular actions of some players in an industry to invalidate everything that comes out of it. (such as implying that anything produced by a startup is ipso facto healthier than something produced by a large pharmaceutical company)
No, because "Big _____" is a Progressive catchphrase that is normally used to villify whatever their target is and rationalize taking away some freedom from the marketplace, wheras "mass produced" just means "mass produced."
Of course, some people might use "Big _____" in a useful way, but it's definitely like a code smell but for English.