Well, considering that there are many strong cards in the BM deck (getting the only knight would be pretty good) aside from villages, there is such a large upside of getting 1-3 good cards out of it that it may still be a good strategy.
Let me put it this way and for fun assign some numbers:
- (double) Jack is solid, sure, let's say it's a 6.5 100% of the time, for an average of 6.5
- There is a large upside to getting some good cards from the BM deck, so let's say it's an 8 50% of the time
- The downside from revealing bad cards from the BM deck might not be that big, you can always go with some BM-Jack hybrid, so let's give it a 5.5 50% of the time
The average from the last two is 6.75 (obviously I assigned the numbers to make the result that way), a tiny bit higher than double Jack.
The numbers themselves are not important, they are just to illustrate the point that by going with BM you might not sacrifice that much (compared to double Jack), but stand to gain a lot if it does go well.