My full understanding of the OSHA standards in the US is that the employer of the lift truck operator is the one that is ultimately responsible for qualifiying (aka certifying) an operator for their specific operations. Live outside trainers provide an educational opportunity for drivers to improve their knowledge & some basic hands on operational skills. On line training only accomplishes the first portion up to a point, i.e. very little opportunity to have alive Q & A session or discussion with others that have a similar occupation.

Lastly, OSHA does clearly state that the operator must be trained in they oprations they are expected to peform - no on the job "trial & error" training allowed around other employees. This means if you are training to perform duites on the shipping & loading dock and you are transfered to the warehousing operations you must be requalfied by the employer to perform those operation , even though it may be the lift truck make, model & specifcations. Change employers the oprator needs to be requalified my his new employer. This sort of like the apprenticeship training that is found in Germany (i.e. a jouney man machinist at company X moves to company Y as a machinist - they are expected to go through apprenticeship training under the standards of the new company - generally this takes 5 years - job hoppers are not common place).
Do really think on-line training can do this, it may be a short course in the total amount of training required in for proper qualification. In a nutshell, most proffessional & live trainers run the operators thru classroom & hands on opertional training - does evaluations at key points and a final exam, makes his recommendations to pass or fail, present the results to supervision/management - along with some paper work (wall certificate and wallet card) stating certain drivers passed his evaluations. And from that point it is up to the employer to provide the job evaluation evalutation and issue the paperwork to the operators as the employer sees fit.
This is basically what guys like Dan M do & I am more than sure he can expand on & will on what I have stated here as I have only provided a Readers Digest "Short Story" based on my own experiences and recalling Dan M posting on this site & his proffessional passion for a career he enjoys plus he trades in his Lambo every year on a new model with the all the latest tech but he has to get requalified each year before he can drive in the US - the word is out on those guys from mostly North of the US - their normal & polite behavior changes when they find warm weather and "fire water" at the same time.
PS: There maybe a typo or two in this message but that is OK by me - I am retired, I am not seeking a grade from a teacher or proffesor or receiving a 5 star performance review from a supervisor / manager and I drive a Fix Or Repair Daily vehicle w/ 270K miles - my wife has the real good car that i am allowed to chauffeur her around in w/cap an all - she calls me Max. This is just free stuff from what I learned along the 41 year journey in the lift truck industry. If this stuff helps great, if it doesn't use the Control-Alt-Delete keys. (LOL)