Hi,
I don't know how BYO predicted the OG, but its pretty easy to verify this calculation by hand, and it does come out to 1.047. You can refer to Daniels Designing Great Beers or any number of other books to get this.
For the two big extracts, take the potential of each extract (1.044 for example), subtract one and multiply by 1000 which gives you the fractional points (1.044 => 44 points) contributed by that addition. Multiply by the number of pounds of extract (44 points * 2.5lbs for example) to get 110 points for the first addition, 118.8 points for the second extract. The steeped grains don't add much - only 6.5 points all together (steeping is generally < 10% efficient at contributing points).
Add these together and you get 235.3 points contributed by the grains. Now just divide by the number of gallons (5 gallons) and you come out with the number of points for the overall batch which is 47.0 points, or a OG of 1.047
That's how we used to do it in the old days...so 1.047 is the correct OG estimate.
Cheers,
Brad