Goldbach Conjecture and Busy Beaver numbers? Background: I am a complete layman in computer science.

I was reading about Busy Beaver numbers here, and I found the following passage:


  Humanity may never know the value of BB(6) for certain, let alone that of BB(7) or any higher number in the sequence.
  
  Indeed, already the top five and six-rule contenders elude us: we can’t explain how they ‘work’ in human terms. If creativity imbues their design, it’s not because humans put it there. One way to understand this is that even small Turing machines can encode profound mathematical problems. Take Goldbach’s conjecture, that every even number 4 or higher is a sum of two prime numbers: 10=7+3, 18=13+5. The conjecture has resisted proof since 1742. Yet we could design a Turing machine with, oh, let’s say 100 rules, that tests each even number to see whether it’s a sum of two primes, and halts when and if it finds a counterexample to the conjecture. Then knowing BB(100), we could in principle run this machine for BB(100) steps, decide whether it halts, and thereby resolve Goldbach’s conjecture. 
  
  Aaronson, Scott. "Who Can Name the Bigger Number?" Who Can Name the Bigger Number? N.p., n.d. Web. 25 Nov. 2016.


It seems to me like the author is suggesting that we can prove or disprove the Goldbach Conjecture, a statement about infinitely many numbers, in a finite number of calculations. Am I missing somehing?
The statement is about infinitely many numbers, but its demonstration (or refutation) would have to be a finite exercise. If possible.

The surprise may come from the (false) assumption that finding BB(100) would be a "theoretically easier" problem, only made impossible for practical reasons - since there are so many machines, and they can run for such a long time before stopping, if at all - after all, they're just machines...

The truth is that discovering BB(n), for n large enough, has to be an unsurmountable task, for both theoretical and practical reasons.