You're right - DNA methylation is inherited (see epigenetics). So DNA alone does not give you enough information.
And methylation patterns are believed to affect higher-order structure in DNA. This higher order structure has to do with the way DNA is packaged when not being actively read for protein synthesis or cell division. Most of the time it is stored in a tightly coiled form that renders it inaccessible to most of the DNA machinery, and it's believed that the methylation patter on the DNA affects the structure of this compaction.
exactly. from the little i know about chemistry tests, most of them are done blending stuff and adding some reagent and see if that changes color or something else that is measurable.
I have no idea how they 'check' dna pairs, but i doubt they compare every subtlety of the molecules every time. If they do, wow! but still, we may not be able to accurately detect something else that is even smaller. since we only saw dna recently. the wikipedia article has dozens of diagrams, but only one blurry 100nm image, from 2004.
Getting back to DNA, we measure information there based on the base pairs. But for all we know, there could be additional sources of information, like some subtle aspect of physical shape that DNA has, that is also inherited (as part of the replication process). Perhaps the amount of information encoded is substantially higher due to that.
(That's wild speculation, of course.)