I think the problem with this thread is that it was a bit "oversold" in the first instance. Perhaps it would have been better to simply describe the event and seek advice.
anyway bringing the subject back on track, passengers boarding via the apron should be supervised. The reasons for this are many, but include the following points:
Engines may be hot and passengers should be kept well away from them; Brakes may be very hot; Accessible pitot, static and other probes may be hot; Ground service vehicles may be manouevering with limited visibility; Fuelling zones must be kept clear; Baggage and catering areas must be kept clear; Maintenance areas must be kept clear.
Nobody wants passengers ( or any body else) to get burnt, or injured from something dropping on them. Consequentely those areas that are deemed as dangerous should be cordened off or supervised from those persons with no specific need to enter them. Having said that there is normally no blanket restriction that prevents passengers from walking beneath a wing ( an airline may have its own of course), other than where the size and shape of the aircraft may compromise the task. On aircraft types with long wings high off the ground, usually found on most airliners, there is no specific danger associated with walking under some portion of the outer wing provided it is well away from engines, wheels and the other zones already mentioned. So this doesn't in itself necessarily constitute a breach of safety , "staggering" or otherwise.
The fact that you are concerned should be addressed to the airline concerned or the airport operator. Any problems that are concerning their passengers and customers would undoubtably be addressed and where necessary investigated to ensure that no deficiency actually exists.