link only states it was a "two cylinder car", so that would make it non-T, but what is it? Sure has a model T look to it at first glance.
That may be a car on the way to Crater Lake, but I'm skeptical about it being the two-cylinder car of 1906 or the 1907 second car. The styling looks to me more like something from the early to mid-teens.
I don't think the photo was meant to match the narrative.
If you had the original photo in front of you, with a magnifying glass you could probably get the year off of the dealer plate that is on the back of the car. The first state issued Oregon plate was 1911. Oregon plates had a vertical "ORE" on the left and the vertical year on the right from 1911 through 1919. White on black was the color scheme for 1914 and 1917. The photo was most likely taken in 1917.
Even though the scan isn't the greatest, it looks like a Dodge to me - profile of front and rear fenders, location of headlight in relationship to fender and the low hood.
Based on this is was a Reo 22hp 2 cylinder:
My maternal Grandmother and 3 of my uncles got the last homestead in Oregon in 1936, straight south of Crater Lake, near Calif.
The pic on the left was Uncle George on the road to Crater Lake. The other pix were taken earlier in Nebr. The ad for the Kelly Tire dealer was in Scotts Bluff. That's my Mom on the left, and her spinster sister. I have a clearer pic of that one somewhere.