The Atlas manual says slab must be 4" MINIMUM thickness of >3000psi concrete, 6" thickness preferred.
Yup, that sure sounds like you will need to pour piers/footings for the lift posts.
Atlas calls out for a 4 ft x 4 ft x 6 inch thick 3000 psi minimum concrete pad keyed to the existing slab if the anchor bolts don't tighten to 85 ft-lbs installation torque (page 6 step 5 of the aformentioned manual).
By the time you take into account the minimum edge set-backs for the anchor bolts and the post-to-post spacing, if you poured two piers for the posts you'd end up with about 4 ft between those two piers of old 'floating' slab. For the about extra 1/2 cubic yard of concrete that that would take (pouring the piers/slab at 12" thick), I say to just cut out one continuous rectangle out of the old slab and then pour the new pier/slab as a continuous rectangle going 'across' from post-to-post. A roughly 4 ft wide x 12 ft long x 12 inch deep slab is still going to be under most redi-mix truck 'minimum' orders at not even 2 cubic yards of concrete. So you'd usually end up having to pay a 'short' fee/cost as well. By this point, you might call and check your local redi-mix places as to their 'minimum' order size and then maybe just go and pour a bigger and thicker 'slab' than the post minimums in order to not end up paying a fee/cost for less concrete than a slightly larger concrete order would cost.
Putting a lift on top of a 'floating' slab is NOT a good idea. At all.
Because then you have run into the situation spelled out in the Mohawk manual (mentioned above) of putting a lift on a floor NOT directly on the ground (and supported by that ground by 'soil' of a minimum of 2000 lb/ft2 bearing strength).
Doing things outside of the manufacturer's recommendations means you pretty much need to get 'experts' involved. Not folks from a forum on the web. Experts as in soils engineers, structural engineers, that sort of thing. Folks who would put their STAMP (actual licensed stamp imprint) of approval on the design, backed up by their education and reputation and knowledge and liability.
Still not sure? Although you called Greg Smith Equipment Inc., the person you talked to said flat out that they were not an engineer and that his 'opinion' was that things should be 'ok' as is. Call him back and ask him to put that in WRITING that it is OK to put their 10K 2-post lift on a slab of unknown compressive strength that is less than 4 inches thick and that has at least a 4" void underneath the slab. Bet you that the person who previously said it was all 'ok' will NOT put all that in writing.
It doesn't have to race or fly, so overkill is a GOOD thing. Make it stronger than the 'minimums' and then you don't have to worry about it at all.
btw, Mohawk puts even more restrictions/qualifications on slab work for their 2-post lifts than Atlas seems to. Mohawk calls for 4000 psi minimum concrete, as well as minimum required rebar specs in that concrete. And that if the existing concrete slab does not meet their specs, that a new slab going 'across' from post to post be formed 12 inches deep and 4 ft wide MINIMUM and length goes 'past' the posts (actual length depends on the model of lift under consideration). Mohawk further calls out that 'no hand mixed concrete is to be used', ie they want a concrete company to have a material cert/spec and paperwork for same to 'prove' that the concrete meets their minimum 4000 psi requirement.