How is a pro-business ideology remotely justifying government intervention in the practice and moderation decisions of a private company? Wouldn't the rectification involve the government specifically dictating their business behaviour?

Most people don’t dive deep into ideologies. They stay in the surface and end up believing whatever the media outlet expresses as a “truth widely acknowledged”.

Also, the concept that businessmen contributing to libertarian causes are in it so that they can capture regulatory agencies/contracts/etc misses that a lot of companies just want the government out of their way.

Whereas with big government, they'll never ever hire lobbyists to ask for bailouts, subsidies and protectionist legislation...

Roads: In general, I prefer privatized roads, like the 407 near where I live. If roads are to be built they should be financed by individuals, corporations, counties, townships, and regions. Ideally these would be funded by donations. Social pressure could be used (ie, a Google map of every house that didn't pay its share of the cost) to expose to the community who the cheapskates are, but tolls at city entrances are fine too. I could talk all day about an ideal libertarian state with contracts being enforced everywhere, but for practical purposes this is a non-issue once brought down to the township and one of the last things that would be worth privatizing. Take the example of an enemy of yours buying up all the land around you and stopping your freedom of movement, do you not have right of way to leave? The way these things should be paid for if they are to be done by the government is through the rent of land from the government. No one created land. No one can morally claim first ownership of it.

Radio: Radio should be treated like property. Rented from the state, just as land should be. People have the right only to jam the radio signals within their own airspace, no further. The state has the right to enforce destruction of property.

National Defense: No standing armies. Lots of nukes paid for through the rent of land. Make it a impossible for another nation to attack you. When all you have is nukes the whole world knows how you will respond to an attack. Voluntary organized (by the government) army and navy reserves for responding to national disasters and enforcing national waters.

Rat Poison => Tylenol: Fraud. Murder. The problem with the FDA is the "F" and the whole idea that they can stop a fully informed adult from taking a drug because it doesn't have their stamp on it. This could also be done through organizations like Consumer Reports. Quibble: Do people sell street hot dogs with rat poison in them? No. People are generally good and we don't need to assume Rat Poison is behind every Tylenol bottle. We would save more lives by subsidizing vegetables (which granted, I'm also against).

Public Schools/Voucher: Ideally donations and paid for by the parents. The whole system needs to be reworked. Why can't I teach math to highschool kids? Oh right. The government says that, regardless of whether or not I'm teaching at a public school, I need to have a teaching certificate. That's a problem. Schools are prisons that only server the bottom 90th to 70th percentile until at least grade 10. But again, this, if done through tax, should be local _only_. No child left behind is a terrible program and a perfect example of letting cities and states be the deciders of education.

When I say pro-government interventionists I (generally) mean the government interfering with mutual exchanges between consenting adults absent force or fraud.

There's a darker strain of libertarians who genuinely don't care whether the congenitally frail receive health care or whether the poor can afford food and shelter, because there's no human right to food and shelter, but there is a human right not to pay taxes. Even most libertarians shy away from this by asserting that somehow private charity will take care of it all, but the empirical evidence is insufficient.

Many libertarians believe that if not for government interference, monopolies wouldn't form in the free market. Those people are right in some cases (e.g. payment processing) and wrong in others (e.g. roads). But the dogmatic position asserts that it's true in all cases, and then no corporation would have sufficient coercive power so you only have to worry about the government.

If you take the practical approach and accept that there are always going to be some private monopolies and oligopolies, or even the pragmatic approach that they actually exist today and we have to deal with them today even if the wonder of the free market will eliminate them in the future, then we have to hold sufficiently coercive corporations to the same standards as governments. And at the same time try as hard as we can to destroy their coercive power, so that we can stop needing to do that.