If you read both the court's opinion and the dissenting opinion, you'll see that the dissenting opinion is strictly based on interpretation. The supreme court not only attempts to interpret how to apply the law, but determine what congress' intent was when enacting the law.
If you look, you'll see they often specifically refuse to join in footnotes/etc that cite congressional intent or history.
That's the way intent is read in contract law: it's judged objectively (from the position of a reasonable person in the position of the parties at the time of contracting), subjective intentions don't matter. [Edit: while true of English contract law, this is apparently not accurate for US contract law: see DannyBee's reply]
(I'm only guessing - I'm an English law student, so not familiar with US supreme court justices, so could be completely wrong on what they're doing. [Edit: yup, I was.])
English contract law is a bit different than US. In the US, it's not objective in general (contracts are held against the drafter, and subjective intent matters).
Your description of objective intent is well, not intent in this case :) Objective intent of congress would be what a reasonable person making the statute would have meant, not what a reasonable person reading the statute would think it meant.
The second is in fact, what is done, but is not related to intent at all, it's related to interpretation.
As for congress's intent, Scalia is of the firm view that either objective intent, or subjective intent does not matter. The words mean what they say, and say what they mean, and if they don't, that's a problem for the legislature. In cases of ambiguity, he believes in plain meaning, not objective intent. So he'll use a dictionary, not try to figure out what congress objectively meant.
He's fairly unwavering in the above, though if you look through hundreds of opinions, you can generally find one or two that are not consistent with this.
http://www.claremontmckenna.edu/salvatori/publications/RARSc... and http://scholarship.law.duke.edu/cgi/viewcontent.cgi?article=... are fairly good descriptions of his approach
It is, in part, an explicit repudiation of English common law.
(Note that I generalized. There are areas where subjective intent does not matter, and areas where it does, but it's nowhere near as objective as English law)