So were they drunk or just being playful?
If they were humans the answer would be a bit easier because an increasing number of us - even in New Zealand - drink Amarula Cream liqueur made from the berries, and that surely is alcoholic.
But biologists from the University of Bristol argue that it is nearly impossible for elephants to become drunk or high from eating marulas.
Their argument goes that, as I had already noticed, most of the fruit elephants eat is actually still on the tree rather than lying on the ground, where fermentation would begin. Furthermore, one researcher has estimated that a three-tonne elephant would need to consume about 55 litres of marula juice to become inebriated.
Therefore, they conclude, it doesn't seem likely that any apparently tipsy behaviour - such as that we were witnessing - has anything to do with the elephants eating the silky flesh of barely ripe marulas.
Still, since the herd did appear to be slightly out of control, and it was feasting on marula, our search for the truth went on.
While none of the searching actually took place inside the elephant's hind stomach - where their food sits, undigested, before being expelled - it did involve studying piles of undigested, whole marulas, which park rangers picked out of the elephants' herbal tea-smelling droppings, for us to look at.
Hmm. It was beginning to look less and less unlikely that these giants of the bush were drunk, or high, or anything vaguely verging on inebriated.
Changing tack a little I decided to focus on the marulas rather than the elephants. If you haven't heard of marulas before, you're in good company.
These relatively small fruit only grow in South Africa. And though extremely popular there, they are almost unheard of in most parts of the world.
Marulas are pressed into service to make jams, jellies and fruit salads, as well as enjoyed fresh.
Despite attempts to cultivate marula trees - which can grow for up to 2000 years and still bear fruit - they have failed to respond.
Even in their natural environment, marula trees prefer to grow in a wild, haphazard sort of fashion.
Seeing them grow reminded me of the cork trees of southern Portugal, which do not stand in neat rows but loom large wherever they please, in a hotch potch, self-seeding growing pattern.
Both are big business. Neither is farmed in the traditional Western European sense of the word.
Marulas are also the key ingredient in Amarula Cream liqueur which is currently swimming against the downward current of global liqueur consumption .
Earlier this year Drinks International magazine polled 700 bartenders, bar owners and mixologists from 60 countries who reported that over the past 12 months only Amarula Cream and Bols have increased in popularity.
If you haven't tried it, Amarula Cream is often described as the Bailey's of South Africa, except it tastes more like burnished fruit in a smooth creamy mix, due to it being distilled into a spirit and oak-aged for two years, then blended with homogenised cream.
Back on the scrubby dry land, which is the South African forest, marulas are thriving too.
For indigenous Africans, marula season is a time to make a little money from windfalls of the fruit. Unlike elephants, who demonstrate a clear preference for the green to yellow fruit when it is still on the tree, most human consumers prefer the riper, softer fruit once it has fallen.
The hard green outer shell of marulas turns a pale yellow when ripe, and it covers the silky white flesh of a lychee-textured, mandarin-tasting fruit. It contains five times the amount of Vitamin C as an average orange and is thought of by locals in the same vein as New Zealanders treasure Central Otago's intensely orange, richly flavoured apricots and cherries.
But, though marula fruit might be healthy, four park rangers all laughed loud and hard when asked whether there was any truth to elephants getting high on the stuff.
"This rumour is total rubbish," laughed the park rangers, in unison.
One added that herds of elephants make for marula trees as soon as the fruit begins to ripen because it makes for such a welcome change after a nine-month diet of leaves, leaves and ... leaves.
Ranger Steve, who was guiding us, added,"Elephants are extremely playful, extremely affectionate herd animals and the marula is a very nice sweet treat for them."
They may not have been high on marulas but these formidably large, beautiful herd animals were definitely high on life - and on each other's company.
Amarula to the rescue
To celebrate 21 years of Amarula Cream, its makers, Distell, last year established the Amarula Trust whose motto is "Sustaining Communities and Conscious Conservation". The trust's work includes the Amarula Field Guide Scholarship Programme, which sponsors people to attend the South African Wildlife College in Hoedspruit to complete a month-long level 1 Field Guide Association of South Africa accredited course.
CHECKLIST
Getting there: Qantas flies daily to Johannesburg from Auckland and Wellington with fares starting at $3041.
Getting around: Johannesburg is the gateway to Kruger National Park and numerous private game parks which can be reached on a one-hour flight to Phalaborwa. This small town provides easy access not only to Kruger but also to private game parks including Kapama Private Game Reserve.
Hoedspruit Endangered Species Centre is open to visitors and is devoted to conservation, research and a breeding programme for cheetahs, including the rare king cheetah. It is also home to wild dogs, black-footed cats, African wild cats, ground hornbills, sable antelope and other species in need of care and rehabilitation.
Joelle Thomson flew to South Africa with Qantas and Distell, the makers of Amarula Cream liqueur.
