The article uses "privately" since the administration's attempts to get peace talks was off the record. See: general Millie talking up peace talks and then immediately being contradicted by the rest of the Biden administration, like he's not working for them...
What lucky timing! "Russia" attacked Poland immediately after the Ukraine bulked at US attempts to force them into peace talks. "Russia" really saved Zelensky's ass here. Looks like peace talks are off the table and the NATO money will keep flowing!