What would you think this phrase meant?

No. Lots of places that take Visa, MasterCard, and even Discover do not take AmEx. Their merchant fees are simply too high.

Never leave home without it. And without another card. If you want to see a cashier in a no AmEx card place freak out, have her ring up a full cart load or more of items, and then say “I only have my AmEx card.”

ETA: The two credit card questions I get asked the most are “Do you take American Express” and “You only take Visa, right?” We will take anything (Visa, MasterCard, Discover, Check, Store Credit, Store Giftcard or Cash) BUT no AmEx.

Aside question: Has anyone found a retailer in the last, say, 20 years which took either Visa or MasterCard, but not both? I’m mostly asking about the US, but anyone with other-country experience is free to chime in.

I carry at least one of each and I can’t say I’ve ever noticed a place which took only one of those two.

“Take Visa” is street code for something illicit.
With a knowing wink and sly tone: Oh sure, they “take Visa”

Or maybe they take only Visa, but the someone knows you only have a MasterCard and MAN is that unfortunate for you!
Oh sure, they take Visa (but you haven’t got one, have you.)

I’d always come prepared for #3, no matter what I think the phrase meant.

Well, the origin of the OP was a nearby bank that only accepts Visa in their ATMs. I commented to my husband that if someone said “We/they take Visa” I would take it as a generic statement about Visa and Mastercard. I wondered if anyone else would. That’s all.

My reaction would be – well they clearly have some agreement with Visa in which they are paid to advertise Visa to me but that probably has nothing to do with what payment they accept.

This exact scenario caused problems in one of the numerous Port Of Spain groceries, I asked a clerk specifically if they took debit or credit cards. And she replied we don’t accept VISA, I assumed she meant we do take them but not VISA cards. No problem for me as I had a mastercard and a local debit.

Yep, you figured it out VISA is slang for ALL credit and debit cards, they only took cash.

What what I think this phrase meant? If I ask a question of a generalized nature, and I get a narrowly specific answer, I tend to think it means that I need to ask it again, more specifically, e.g., “what credit cards do you take (or do they take)?”

I would assume they meant #2, but I’d expect #1 anyway, since it’s 2014 and all.