Do tubeless tyres explode more easily than standard one?
TLDR - I have been commuting daily on tubeless tires now for about 3.5 yrs. In my 20 years of daily cycling experience, I have had a number of tubed tires spontaneously rupture due to heat, especially if a wheel set was left in the back of a car! I haven't had a tubeless tire explode yet using tubeless specific rims and tires.

Hypothesis: Previous damage
My best guess is that the tire was already  damaged (e.g., road debris causing a partial cut that could be re-sealed) and then the added heat could have caused it to rupture. A damaged tire casing can undergo rapid decompression regardless of whether you are running tubes or tubeless.  In the case of tubes, if the tire cords (the internal structure that actually counteracts the force from the pressurized air)  gets damaged the tube can escape out of the tire carcass and rupture as a result.  Similarly, in the case of a tubeless setup, if the tire gets damaged in such a way that it can no longer support the pressure, a the tire would rupture in a very similar way as a tubed tire.
What about the shop's claim?
Tubeless tires can also rupture if their is an unsuitable tubeless tire/rim combination. For example, in the early days tubeless specific rims were rare, so people often converted regular rims to a tubeless setup.  It can be done, but the tolerances are not as good, one problem is that the tire bead can climb over the rim hook if pressure is too high for the tire/rim combination (many wheels are slightly undersized (i.e., out of spec) for easy of tire mounting).
With a tubed tire this is less of an issue as the friction against the tube helps to prevent the bead from climbing, even if the rim is slightly out of spec.
Ad hoc tubeless setups were also less of an issue in mountain biking because mountain bikes run lower pressures. That said, tubeless is still a bit of a wild west when it comes to road tubeless. There unfortunately isn't a single standard and some wheel/rim combinations (even if specified as being tubeless) can fail under high pressures.  Further adding to the confusion people may also be experimenting with &quot;road tubeless&quot; with regular road rims which will be highly unsuitable due to the higher pressures typically used on road tires.
I suspect these issues may be what the shop was referring to, but it's hard to assess as we would need to directly speak to them.
That said, I don't think this was you issue.  In your description you also described the tire has having a gash, as such I suspect the tire failed due to damaged as was described above, not from a poor tire/rim combination.
As such, the shop's claim may be a bit of a red herring in terms of your described experience.
So are tubeless more dangerous?
I doubt it. Anecdotally, I have been commuting daily on road tubeless tires for about three years, including one tire that had a partial sidewall gash that resealed (descending too fast on very rocky gravel trail), and never had the tire explode like you describe. Furthermore, I have never had a flat tire in those three years.  I would suggest, that there is higher &quot;risk&quot; with tubed tires, as getting an unexpected flat can easily cause a crash.
In terms of your experience, if this was the result of tire damage, it was likely the culmination of a number of low probability events.  Partially damaged tire, that resealed, then increase pressure due to heat that didn't cause the sealant plug to fail, but initiated a structural tear in the tire due to the earlier damage. Because of the low probability of these events it is hard to assess how likely this type of event is by tire type.