It's not so much the claim itself that bothers me. More the attempt to blur the lines and make it more difficult for the uninitiated to tell the difference between what's on offer. It feels to me like that was the intent behind it.
As others have already pointed out, they're not likely to get many new customers from advertising. So the only reason I can think of why they would want to broadcast this message is to influence the mindset of the customers they already have. They don't want to lose their fairly dominant position in the market, so it's in their interests to convince people that they've already got everything they need. It's better for Visa if people aren't looking at other options, so they want to give people the false impression that Visa is offering all the same benefits as the competition.
I know pretty much all advertising is dishonest in one way or another, but this just seems more pernicious. Like they're co-opting the narrative. Using our own words against us to make it sound as though we can't offer people anything different.
Well, that's basically an advertisement is, trying to make you think that they are the best option for your own good whereas they are only caring about money. Like do you really think that Apple cares about making world's greatest phone or computer? That's by-product of what their real aim is, they want to make a lot of money, if you told apple that they could make a horrible phone for 1 dollar each and sell it for 1000 dollars then they would do that, they wouldn't just make a good phone out of their own good heart, they would make a horrible one and sell it for very expensive amount and get rich, however they know that there is competition so they need to make a good one in order to profit.
Long story short, it is basically just same situation for Visa, they are trying to make it look like you should use Visa because it is good for you, but the reality is you should use it so that they could make more profit.