The National Park Service - American Battlefield Preservation Program has this battle shown as:

MIDDLE BOGGY DEPOT

I have never hear of "Middle Boggy Depot". That term is not used in the ORs. I assume this is a mistaken combination of "Middle Boggy" Creek and "Boggy Depot". I would be thrilled to learn there is such a place on the Middle Boggy near the Chickasaw-Choctaw border.

The site incorrectly states:

"During Col. John F. Phillips’s Indian Territory expedition..."

The Union commander was, of course, William A. Phillips.

A sentence that can be misleading is "Fear of the arrival of fresh Confederate forces influenced the Federals to retire to Fort Gibson." This is correct as to the expedition. As to the battle, Willetts held the field. Phillips caught up and, it seems, camped at the battlefield (Camp Kansas) before moving south and establishing Camp Kagi on South Boggy (Boggy Creek aka Boggy River).

Below is the full text from
http://www.cr.nps.gov/hps/abpp/battles/ok005.htm

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Middle Boggy Depot
Other Names: Middle Boggy

Location: Unknown

Campaign: Operations in the Indian Territory (1864)

Date(s): February 13, 1864

Principal Commanders: Maj. Charles Willette [US]; Lt. Col. John Jumper [CS]

Forces Engaged: Three companies of the 14th Kansas Cavalry Regiment and a section of Howitzers [US]; Seminole Battalion, Company A, 1st Choctaw and Chickasaw Cavalry Regiment, and a detachment of 20th Texas Regiment [CS]

Estimated Casualties: Unknown

Description: While on an expedition in February 1864 to meet, defeat or destroy Confederate forces in Indian Territory, Union Maj. Charles Willette and his troops surprised a Confederate force at Middle Boggy Depot on February 13. Although poorly armed, the Rebels made a determined stand for a half hour before retiring. The Union forces killed 47 Confederates during this short fight. Fear of the arrival of fresh Confederate forces influenced the Federals to retire to Fort Gibson. During Col. John F. Phillips’s Indian Territory expedition, he and his men fought with and dispersed numerous Confederate forces. Middle Boggy Depot was, perhaps, the largest encounter during the expedition.