I agree with that... it don't matter much because most birch and (native) cherry's carry about the same BTU per cord, 20-million. That doesn't look like Black cherry we have 'round here, Chokecherry is much smaller, more like a bush than a tree. I don't believe Black Cherry is natural once you get very far west of the Missouri River. On the other hand, your pictures resemble birch, but I believe the only birch natural to Washington is the Paper Birch... which normally has bright white bark.
I'm thinking the FIL is correct,
it is cherry not birch. Most people in the U.S. wouldn't be familiar with the breed of cherry I believe it is because it's more common in Canada. But it is found in some of the more northern states, like Minnesota, Wisconsin, North Dakota, the extreme northeast, and, yes, Washington. We have some here in N.E. Iowa (I was looking at some last night)... It's called Pin Cherry (sometimes Live Cherry), here's some pics...