The Minutes of Virginia's Conference With the Indians at Logstown (June 1, 1752) and Governor Robert Dinwiddie's reports to the Board of Trade (Oct. 6, 1752 and Dec. 10, 1752) demonstrate the international context of negotiations with tribal leaders on the Ohio River frontier. As Dinwiddie noted in his October message:
The colonial Virginia governor in Williamsburg cared about the political allegiance of the Twightwees on Lake Erie because the Virginians claimed the Ohio Territory was part of their colony. Before Dinwiddie picked a fight with the French by sending George Washington to the Forks of the Ohio, the English had conspired for several years with various Indian allies to limit the influence of French traders in the Ohio River Valley.
For example, the English stimulated construction of a new settlement, Pickawillany, on the Great Miami River near modern-day Piqua, Ohio. It housed the Miamis who had abandoned the French and allied with the English. The leader of that group was La Demoiselle or "Old Britain," so named for his loyalties to England. The French destroyed it (and their Indian allies literally ate Old Britain's heart...) on June 2, 1752, a date which could be defined as the start of the French and Indian War.
Both French and British traders were actively seeking allies along the Ohio River in the late 1740's and early 1750's. As soon as Celeron passed downstream in 1759, British traders from Virginia and Pennsylvania tried to counter the impact of his visit. The Ohio Company - technically not the colony of Virginia - sponsored Christopher Gist's visits, which he documented in a journal of his 1750-51 travels.
The British "right" to the Ohio River watershed was based on the claim that the English had conquered the region. The English troops had not entered the region, but the Iroquois acceptance of the Treaty of Lancaster in 1744 was defined as a sufficient proof of conquest.
The French based their claim by right of discovery. Baron de Longueuil travelled from Montreal to what later became Memphis in 1739, mapping the Ohio River for the first time. A decade later in 1749, Pierre Joseph Céloron de Blainville travelled down the Ohio and deposited several lead plates establishing the French claim.
Of course, the Native Americans had established trails across the region for perhaps 15,000 years... but that claim could not withstand the French "incentives" for trade or the English pressures for settlement.