There is some concern about moderate side to side and front to back sway when resting on jacks only. There are a couple of brands of horizontal stabilizers available to mitigate that. However vertical weight on the jacks is of little concern (to me). The key is in how the jacks are attached to the camper. Corner brackets attached with screws to the frame should be plenty strong considering the sheer strength (greater than 1000 lbs per screw) of the screws. There is some slight concern over screw pull out in the case of lateral movement but this is minimized by the number of screws used to attach the brackets to the camper frame assuming that the wood is in good condition.
However the older tripod (three jacks as opposed to four) jack system would not be stable enough for camper use while unloaded.