Is there a reason to doubt this ID is correct?

Some authorities list it as B. pendula, others just call it Betula 'Trost's
Dwarf.' There are some technical problems with it being B. pendula, but I don't
have any details.
The URLs you mentioned are not taxonomic authorities, & the botanical
references don't mention cultivars.
Iris,
Central NY, Zone 5a, Sunset Zone 40
"If we see light at the end of the tunnel, It's the light of the oncoming
train."
Robert Lowell (1917-1977)