We have a judicial system to deal with issues like this which generally handles things fairly regardless of the size of each party.
However, in the day and age of modern logistics I'd argue that their suppliers could have sold to other customers in other states.
Ultimately I suppose it depends on how we define a market (ultra regional or wider) and how high the transaction costs (+other extra costs) of the suppliers would be to move to another customer. The classical example in "The Economics of Imperfect Competition" was the labor force in a small town (mining iirc., once again not at my bookshelf). I suppose that would give precedent to the fact that small markets "count". However most studies on the topic I am aware of are about labor not supply/demand structures. And I'd argue it is "easier" for a supplier to move their wares to another customer than for a (specialized) worker to move to another company (uproot family etc.).
Additionally some of the suppliers of Walmart are in pretty strong negotiating positions themselves (Unilever etc.).
At least there's enough doubt in my mind to say Walmart's supplier relations are "a textbook example of a monopsonist".