I wonder what would happen if one was to inform such a restaurant that "if you're not in a position to accept payment using the card for which you display the acceptance logo and paraphernalia prior to purchase, I am not in a position to make payment"... Would be interesting to see the response. I don't think I'd be game enough to actually try it though
One could argue that it would amount to "engaging in conduct that is misleading or deceptive", in contradiction to Section 52 of the Trade Practices Act 1974 - as they were pretending to accept payment methods that they were unable to process, and only informing you of the situation after you had already entered into a transaction with the merchant. As such, you would be under no obligation to pay using another method if the restaurant had advised prior to the transaction (in this case, dining on an 'eat now, pay later' system as most restaurants support) that American Express cards were welcome (either verbally or visually through the 'cards welcome' decals or logos). You would however be obliged to supply your name and contact information in such a case, and you could invite the restaurant owner to contact you when they were ready to process your payment (either once they had found their imprinter to send a manual voucher to Amex, or once their EFTPOS terminal had been correctly updated to process Amex payments).
I've made the threat once before, and when challenged for another card, I pulled two more out - both were Amex cards also... turns out the business owner 'happened' to know that the shop next door (which seemed to be owned by the same family/group) had a mobile terminal that supported Amex, and processed the payment that way... he wasn't going to get paid otherwise! The business owner next door didn't seem too concerned by it - his body languaged implied that it wasn't the first time this had happened.
If a business shows the logo, I expect to be able to use the card. If no logos are displayed (or only Visa & MC logos are visible), I always ask first and am prepared to walk unless there is no reasonable alternative available. I'm the argumentative type though and am pretty thick-skinned, so those who are more shy or introverted may be more inclined to just pay with another card (which also wouldn't be a bad idea if you're on a date haha!). As I earn 3x the number of points on my Amex when compared to my MasterCard, MasterCard is not an option if they have advertised Amex acceptance
EDIT: It could also be in violation of Section 53 (D) of the same Act:
A corporation shall not, in trade or commerce, in connexion with the supply or possible supply of goods or services or in connexion with the promotion by any means of the supply or use of goods or services-
(d) represent that the corporation has a sponsorship, approval or affiliation it does not have;
NEWER EDIT: Was just buying some advertising on Facebook for my business, and only Visa/MC are accepted for $AUD transactions... however, if you change the currency to $USD, both Amex and Discover (Diners) become available - you just price your ads in $USD instead.