Okay, the theory seems to have more going for it than at first sight - particularly the facts that there were (apparently) travelling circuses which went through the area, and that the theory isn't that there is actually a feral population of elephants heretofore undetected on the shores of Loch Ness. The guy putting forward the theory also links the £20,000 reward for capturing Nessie offered by Bertram Mills in 1933 with the theory, stating that the showman may well have been very certain that he wouldn't have to pay up (
link).
To my mind though the biggest problems still with the idea are that there is really no evidence (it's all surmising, 'could have', 'maybe', etc.),
and that many alleged sightings and photos don't fit at all with the Elephant Hypothesis. In fact, a quick flick through a book I have coupled with a Google image search only really turns up two photos which fit the bill (or trunk): the one the OP posted (which, it turns out, was taken in 1972, so apologies for my mistake earlier), and the Surgeon photo, which was admitted to be a hoax with no elephant element at all.
The other (very few) photos, the famous Dinsdale video, and many eyewitness reports don't tally with an elephant at all, and neither does the fact that sightings have been reported from the 1800s to the present day,
apparently. It's interesting when you look through the list of sightings on that and other websites that sometimes the 'monster' is compared to an elephant in some respect; whilst it'd be tempting to take this as evidence for the Elephant Hypothesis, in fact it more likely indicates that those alleged eyewitnesses were familiar enough with elephants to say "colour of an elephant" or "neck thicker than an elephant's trunk", and therefore probably as likely as you or I to know an elephant when we see one. Although there is the problem of context (if you see an elephant in a place where there really probably shouldn't be an elephant, it's easier to make a misidentification I guess).
It would be very interesting to see if there's any correlation between the list of sightings and known times when there was a circus in the area.
I'd personally quite like a nice, convenient catch-all explanation, but I just doubt this is one. Not that I think 'real monster' is a better explanation - my own pov would be that some people saw things they were unfamiliar with; others made deliberate hoaxes or lies; others had pranks played on them; and some people are just weird. Maybe a couple of them
did see an elephant. All of these events centre around the pre-existing monster legend, which as we know isn't uncommon these days around deep lakes (and probably just reflects our own wishful thinking and fear of deep things) and so becomes part of an illusory coherent narrative.