No, that's not true. 4GHz is the single core boost. As soon as a second core is loaded, it drops to 3.9GHz. You'll occasionally see more than one core showing 4GHz in a program like HWiNFO64, but I assume that's just a sensor updating issue, not keeping up with rapid changes. You said it should hit 4GHz on all cores, and that isn't how Intel's boost works. Equally, it isn't true to be saying it should drop below 3.8GHz in any scenario except thermal throttling. The all-core turbo is 3.8GHz. Why would it ever drop below that unless it was hitting thermal limits? I've never heard of any Intel chip exhibiting the behaviour that you're describing, other than when multi-core enhancement is interfering with the turbo clocks (but that doesn't work on locked chips, so is irrelevant in the 8400's case). Or when an AVX offset is set, if we're talking AVX workloads, but that's a recent thing and only necessary when pushing high manual overclocks on unlocked chips.
Incidentally, I had my 8400 running on two different motherboards (an ASRock Gaming K6 and a Gigabyte Aorus Gaming 7) before I sold it, and it performed identically on both of them. No 4GHz on all cores, no drops below 3.8GHz under any circumstance.