Did this actually happen

Yes. Buchanan pressured Greer into voting against Dred Scott to prevent the decision from looking like a purely Southern decision. Once the vote was secured, Chief Justice Taney tipped off Buchanan. Buchanan incorporated [the forthcoming decision into his inaugural address] (http://www.presidency.ucsb.edu/ws/?pid=25817). Republicans pilloried Taney and Buchanan for this seeming collusion, and it destroyed the reputation of the Supreme Court for a generation among Republicans and Northerners. This speech, by an obscure Illinois politician named Lincoln, is fairly representative of the reaction from the North.

How common is such direct executive (or legislative) involvement

By today's ethical standards, it's a huge breach of judicial ethics, and it would get most judges impeached. If you look at most modern judicial codes of ethics, they require judges to "avoid impropriety and the appearance of impropriety in all of the judge’s activities", or have similar statements. The mid-19th century had looser ethical standards, but the idea remains the same: judges are supposed to stay impartial, neutral arbiters of the law and avoid the appearance of impropriety.

So, direct involvement is generally rare. Two reasons why. First, there's a political cost if legislators or executive-branch officials appear to be meddling in supposedly-impartial judicial decisions, as Roosevelt discovered when he tried to add new Justices to the Supreme Court in 1937. (The Justices had been systematically blocking the New Deal, and he wanted to add friendlier faces.)

Second, the courts themselves try to avoid the appearance of giving political favor, because the courts are the weakest branch compared to the Congress or the executive branch and they're just as vulnerable to political pressure as the other branches of government. Alexander Hamilton noted this in Federalist 78. To paraphrase Hamilton, the courts have neither the power of the purse nor the power of the sword. The courts rely on the legislature for funding and rely on the executive for enforcement. And judges know this-- something that Friedman lays out very eloquently.

Partisan courts put their own powers at risk, especially if they go against public opinion. The most obvious examples of this are West Coast Hotel v. Parrish, 57 S. Ct. 578 (1937), where the Supreme Court changed half a century of set jurisprudence under the threat of the Roosevelt Administration, as I noted above. See also Worcester v. Georgia, 6 Pet. 515 (1832), where the Supreme Court's unpopular defense of Indian rights was summarily ignored by President Jackson. Another good example of this is Korematsu v. United States, 65 S. Ct. 193 (1944), where the Court folded in the face of wartime pressure and racism to give their approval to Japanese internment.