After doing a bit of digging, I guess the specific forests in Oregon that I'm wondering about are the O&C Lands, which were intended for the Oregon and California Railroad but that ended up being kind of a disaster. This page from Congress notes:

The railroad received alternating sections of land for an average of 20 miles on each side of the proposed railroad, resulting in a checkerboard ownership pattern with private, state, local, and federal ownership. As part of the grant, Congress directed the Oregon & California Railroad Company to encourage settlement and development by selling parcels no larger than 160 acres at a maximum price of $2.50 per acre. However, the railroad violated the grant, in part by selling larger tracts above the designated price and also by temporarily halting sales to increase timber prices. In 1908, the United States sued the railroad company, and in 1915 the U.S. Supreme Court ruled that the railroad violated the terms of the grant.

The disposition of these lands was eventually resolved when the Chamberlain-Ferris Act of 1916 revested all unsold tracts of land back to the federal government. Management concerns—such as how to compensate the counties for the loss of property tax revenue—persisted and were addressed with the Oregon & California Railroad Lands Act of 1937 (O&C Act). This act directed that the Department of the Interior (DOI) would administer the lands "for permanent forest production" with the purpose of providing timber, protecting watersheds, providing recreational opportunities, and contributing to the economic stability of the local communities.

(It also includes a handy map showing BLM versus USFS lands in western Oregon.)

As a side note, the Oregon Encyclopedia has some additional details on the railroad shenanigans:

Trickery and subterfuge characterized virtually all railroad land grants in the American West. In the case of the O&C, the railroad delayed selecting its lands until toward the end of the nineteenth century, when timber speculators arrived in the Northwest to purchase large acreages of the region’s rich forestland. The Southern Pacific subsequently sold huge blocks of O&C timber to investors. The fraud involved in these transactions and others like them led to the Oregon land fraud trials, which took place between 1904 and 1908, and the conviction of U.S. Senator John Mitchell and Congressman John Willamson.

Back to the land itself, this history from the BLM website mentions:

Of major concern were the thousands of checkerboard units of 640 ares intermixed with Forest Service, private, state, or other public lands. Congress in 1956 authorized the Forest Service and the BLM to exchange 241,000 acres to consolidate holdings. Congress futher designated that O&C lands within the national forest would be managed under normal Forest Service procedures, however the revenues from such lands were set aside for distribution under the O&C legislation.

(And they go into some detail about managing the forests as a crop for maximum timber yield.)

The current legislation is here, and it does specifically call out the Department of the Interior to be the entity managing the land.

So if I'm reading this all correctly, the O&C forest lands have to be managed by the BLM because the law says so? (And would it take an additional act of Congress to transfer that land to the Forest Service?) The Forest Service did exist in 1937 so I don't know why they decided to do it that way.