I wonder if that information could ever really be untangled by a civilisation starting entirely from scratch without access to a cell

Coding DNA and non-coding DNA looks very different. Proteins are full of short repetitive sequences that form structural elements like alpha helixes: https://en.wikipedia.org/wiki/Alpha_helix

Once you've identified roughly where the protein-coding genes are it would be trivial to identify 3'/5' as being common to all those regions. You could pretty easily imagine a much more complicated system with different transcription mechanisms and codon categories, but earth genomes are super simple in that respect. Once you have those you just have the (incredibly complex) problem of creating a polymerase and bam, you'll be able to print every single gene in the body.

Without the right balance of promoters/factors/polymerase you probably won't get anything close to a human cell, but you'd be able to at least work closer to what the natural balance should be, and once you get closer to building a correct ribosome etc the cell would start to self-correct.

But… doing so from first principles without a mental model of how all (human) CPUs work? I guess it comes down to whether the recipients had enough context to know what they’re looking at.

In genomic science we nearly always use more cheaply available information rather than attempt to solve the hard problem directly. For example, for decades, a lot of sequencing only focused on the transcribed parts of the genome (which typically encode for protein), letting biology do the work for determining which parts are protein.

If you look at the process biophysically, you will see there are actual proteins that bind to the regions just before a protein, because the DNA sequences there match some pattern the protein recognizes. If you move that signal in front of a non-coding region, the apparatus will happily transcribe and even attempt to translate the non-coding region, making a garbage protein.

Based on the way the person is using it, it does not seem to equate to the Kardashev scale, as my peer stated

Humans are currently LR2 (food security) and approaching LR3 (artificial general intelligence, self genetic modification). LR4 is generally associated with multiplanetary homing (IE, could survive a fatal meteor strike on the home planet) and LR5 with multisolar homing (IE, could survive a fatal solar incident). LR6 usually has total mastery of physical matter, LR7 can read remote multiverses, and LR8.2 can write remote multiverses. To the best of LR8's knowledge, there is no LR9, so far as their detectors can tell, but it would be hard to say, as LR9 implies existence in multiple multiverses simultaneously. Further, faster than light travel and time travel both remain impossible, so far as LR8 can tell.

“An Outside Context Problem was the sort of thing most civilisations encountered just once, and which they tended to encounter rather in the same way a sentence encountered a full stop.” ― Iain M. Banks, Excession

“Unbelievable. I’m in a fucking Outside Context situation, the ship thought, and suddenly felt as stupid and dumb-struck as any muddy savage confronted with explosives or electricity.” ― Iain M. Banks, Excession

“It was like living half your life in a tiny, scruffy, warm grey box, and being moderately happy in there because you knew no better...and then discovering a little hole in the corner of the box, a tiny opening which you could get your finger into, and tease and pull apart at, so that eventually you created a tear, which led to a greater tear, which led to the box falling apart around you... so that you stepped out of the tiny box's confines into startlingly cool, clear fresh air and found yourself on top of a mountain, surrounded by deep valleys, sighing forests, soaring peaks, glittering lakes, sparkling snow fields and a stunning, breathtakingly blue sky. And that, of course, wasn't even the start of the real story, that was more like the breath that is drawn in before the first syllable of the first word of the first paragraph of the first chapter of the first book of the first volume of the story.” ― Iain M. Banks, Excession

Or do you mean that a civilization at a particular level will always be unaware of civilizations above? That doesn't seem to make sense either; I see no reason why a LR4 civ couldn't have knowledge of a LR5 civ, for example.