That was Remington's '308 Competition', also known as 308 UBBR (Unformed Basic Bench Rest) brass. It was made for reforming into the various versions of the BR Remington which had only just been introduced sometime in the 1960s. Hence the unusually thin walls to facilitate reforming. Back then, you had to buy form-dies to make your own BR cases as Remington didn't produce any or loaded ammunition (nor anybody else for that matter). (In fact, they never did other than for a period many years later when 7mm BR Rem became a popular metallic silhouette / single-shot pistol number and was offered as a factory ammunition product.) As you say, they not only had small primer pockets, but the smaller diameter flash-hole.
Naturally, many keen shooters learned about these cases and tried them in the 'basic' 308 Win form or in various wildcats based on the 308 case. The primary attraction wasn't the small primer ignition, rathe the thin walls which gave the case an unusually large capacity. As a rule, it didn't work out well for most who tried this, apparently through inadequate ignition - large ES spreads, hang and misfires were widely reported. Many users drilled the holes out to standard size and obtained an improvement.
So, when the US Palma Teams got together with Lapua back ca. 2008/9 to have a run of experimental small primer / small flash-hole cases made, and range-tested them over a season, the US Palma Teams' Long range Forum was inundated with posts by sling shooters who said it wouldn't work, in many cases from their own experience. Not only did the combination now work, but Lapua put this version into its catalogue and it has been widely used by F/TR, Palma and Fullbore shooters in many countries since 2011 or thereabouts
There is no reason to doubt the experience of the naysayers and their genuine concerns, but it seemed something changed to powders and Small Rifle primers early this century which changed a marginal situation into an acceptable one (with most powder grades anyway). The reason that the Palma Teams decided to experiment was that a team member, whose name I can never remember sadly, collected stocks of the Remington 308 Competition brass and competed very successfully using it over a couple of seasons. He persuaded the team managers to look at the concept, and they in turn involved Lapua to produce experimental brass. (The close collaboration with the Finnish manufacturer is why Lapua was able to subsequently christen its new case model the 'Lapua Palma 308 Win'. The US teams have trademarked the name and guard it zealously. AFAIK, Sierra with its 0.308 155gn MatchKing bullet and Lapua for this single case model are the only commercial companies who have been granted such permission for use on their products.)
There is a surprising number of these elderly cases still in circulation and many are owned by members of this forum. There is at least one forum member who was on the Palma team at the time and knows the entire story in detail.