There was a much more extensive system of credit-card authorisation, which a Steve Martin comedy is unlikely to show.

Banks had always accepted some risk from fraudulent payments via cheques.

Some countries placed a lot of the risk with the person accepting the cheque, but "travellers' cheques" arose to handle this use-case: they were, once signed, effectively bearer bonds and carried much less risk for the person accepting them. In Europe they were mostly used when travelling between countries, but in the USA they were also used internally, particularly as banks were (are still?) prohibited from operating over state lines.

In the UK, the cheque guarantee card scheme started in 1969, and ran until 2011. That provided you with a credit-card sized card (later, integrated with a credit or debit card) which guaranteed cheques written by the bearer provided the signatures roughly matched. If the cheque were fraudulent or drawn on insufficient funds it was paid anyway. There was a similar system in much of Europe for Eurocheques, which were a sort of on-demand traveller's cheques. Having a Eurocheque book as a UK citizen was seen as terribly sophisticated for about six weeks until credit cards killed the use case, but Eurocheques were very popular in Germany where credit cards had a lot of cultural and regulatory barriers. I recall that well into the 1990s you needed a lot of cash to visit Germany, because outside cities credit card acceptance was essentially zero, Eurocheques and travellers' cheques were viewed with suspicion or were just too much work and local cheques were guaranteed.

[[ As a sidenote: in Holland, Germany and Austria, and perhaps elsewhere but those are the countries I've recently been bitten by it, there are things called Geltkarte or local spelling which are low-value, non-network local payment cards. In some cases, there are transactions you can do with a Geltkarte you can't do with a Visa/MC/etc, in particular low-value local train tickets. The same's true to an extent in Japan: there are a lot of local cards for local people that are accepted in scenarios when your international card isn't. And as an extra note for the outraged American I was behind in a queue in London last week, your Discover card is, for practical purposes useless in Europe. ]]

Cheque cards had a limit per cheque which was low but not trivial: £30 in 1969 was a week's wages for many people, and for many people it was £250 by the time the scheme ended. A cheque card and a book of 25 (or in some cases 50) cheques was a substantial implicit line of credit.

So when credit cards started to roll out in volume in the 1970s, the principle of the issuer carrying some fraud risk was well established, and the banks knew how to model it. What they did was impose a "floor limit" ("floor" in this context meaning "shopfloor") on each merchant, past which authorisation was needed. In the UK that limit was, unsurprisingly, usually at or around the then ambient cheque card limit, elsewhere it was set by the processor. Payments below that were accepted and (usually) the issuer or (sometimes) the processor stood the risk provided the merchant had not been grossly negligent. The credit card companies and banks had to do that, as otherwise many merchants would simply refuse to accept credit cards, and the product would wither on the vine.

Various side-shows were tried (for a while in the 1990s I had a credit card with my photograph on it, although I don't remember anyone checking it) but the basic premise was "small transaction, accept the card, risk is with someone else".

For larger transactions, the merchant had to phone their processor for authorisation. That worked on a sort of triage system: there was a national (global?) list of stolen or hot cards, which all the processor had (and in fact for the very hottest cards, the merchants sometimes had it). After that, they tried to contact the issuer to see if the card was good (not stolen, not over limit, etc) but if it timed out they took a risk managed approach to granting authorisation and thereby accepting the risk either themselves or on behalf of the issuer (there was a complex web of contracts, as you can imagine).

This system was progressively automated, and in Europe at least fairly quickly three part impression machines either were replaced by "swipe the card, automate the authorisation, print a two part slip that is signed by the holder, automate the back end" or "swipe the card, get the authorisation, only then use the mechanical device". It's hard to remember, but I've held a credit card since 1982 and so far as I recall three part machines were already in decline in large shops.