Over short time scales, Layer feed is not likely to harm adult birds in ways you are likely to recognize, particularly older adult birds. Excess calcium is most damaging to hatchlings and juveniles. It builds up in roosters and non- (or infrequent) layers over time, the first symtoms you are likely to recognize are often taken as signs of age or injury - things like gout. Opening them up will show yet more damage, if you know what to look for.
I feed my Roos after 8-12 weeks a mix that's about 2.6-2.8% average calcium, more than an All Flock, less than a Layer. I do it for cost reasons. At 18 months, I can usually see internal symptoms in at least some of the roos, though I have yet to see clear external evidence of excess calcium. I butcher early and often, only keep a couple roos to that age, so I can project what is likely to happen with more calcium, or longer time scales, but I've not seen it first hand.
That said, there is no commercial all flock I am aware of which has been reported to cause that incidence of fatty liver - if there was, it would be pulled from the market.
"I don't give much in the way of treats" is, frankly, suggestive that "much" is "too much". Are they able to get feed from sources other than the All Flock and the treats you offer? I.E. do they free range, and what do they free range??