The image that Visa is trying to promote is that they're the most commonly accepted card. Because consumer perks vary only slightly (if at all) in home countries, for most consumers, the question becomes permeation. If they see lots of places accepting Visa and not Mastercard then they're more likely to get a Mastercard.
To give you a closer-to-home example: In Canada, we have Tim Hortons - which is a cheaper version of Starbucks (and it's very popular). They take Mastercard, but not Visa. There have been several situations where I've been unable to purchase food because I use Visa and I hate cash. At no point have I said "damn you, Mastercard! I hate you!" In fact, if I actually drank coffee, I'd probably have gotten a MC already.