The Four Color Media Monitor

Between Superman #76, World's Finest Comics, All-Star Comics, and the radio series, DC ended up with at least four different "first meetings" of Superman and Batman. And that was before Crisis On Infinite Earths and any other reboots or retcons.

Superman helped Batman & Robin on a case in a 1945 episode of the Superman radio show. They had apparently heard of each other, but had not met before. The Dynamic Duo became semi-regular guest stars on the radio show for several years.

Batman and Superman appeared together as honorary members of the Justice Society in All-Star Comics #36 in 1947. Unlike their previous appearance in that title, it was not just a cameo; they actively took part in the adventure. It was reprinted in DC Blue Ribbon Digest #3 in 1980.

The foreword in Superman #76 said that the two heroes had never met before, and DC seemed to consider this their first "official" (canonical) meeting for some time. A flashback in World's Finest #71 also cited it as their first meeting. WF #71 was also when the Superman-Batman team-ups began on a regular basis. Before that, both appeared regularly in World's Finest, but in separate strips.

I wouldn't go as far as to say that DC "pulled a fast one" by having the heroes together on covers before #71, though. In the 1940's, it was common to have characters appear together on covers, but in separate strips inside the comic. Superman, Batman, and Robin in WF, Flash, Wonder Woman, and Green Lantern in Comic Cavalcade, and Captain America, Human Torch, and Sub-Mariner in All-Winners.

World's Finest #94 (1958) had a flashback retelling the team's origin, and it was different from any previous versions. Back then, it was assumed (probably correctly) that the readership turned over completely about every 5-7 years, so DC probably figured a kid reading comics in 1958 would not know about the 1952 version.

WF #179 (1968) reprinted Superman #76, and both WF #71 and #94. The foreword to "The Mightiest Team in the World" was edited, removing the statement that they had not met before. In the Bronze Age, DC canon was that WF #94 told how they first met, and Superman #76 took place later, and told how they first learned each other's secret identities.

WF #271 (1981) tried to reconcile the different versions. IIRC, Superman #76 and WF #94 were on Earth-1, the JSA stories were on Earth-2, and the radio series was a dream or something.