The OP posted the actual wording she (?) used:
And, I was paraphrasing myself earlier. The actual wording was, "if you cheer for me somewhere along the course, I'll buy you dinner at XXX restaurant." I suppose my mistake was in sending the Evite to all and sundry. Maybe I should have just emailed around asking, "is anyone going to be on the marathon course?" and invited only those who answered yes.
That being said, I'll try to think of this as she's happy for me and wants to get together.
OP, I hope the race and your dinner go well.
With the single line, I don't think it's particularly ambiguous, however I doubt the evite really was one single line. So other text may have lead to more ambiguity.
Regardless, I know after reading this thread I for one will be quite careful now in how I word invitations!