So did her employer make any contributions to her HSA or did she contribute to her HSA by means of payroll deductions? If either of those are true, then her employer made a mistake on her W-2.
Yes, code DD is for the sum of what her employer paid for health care premiums plus whatever she paid for health premiums. The code W refers ONLY to contributions to the HSA.
Note that there are a few employers who do a so-called "passthrough" contribution: Some or all of the amount under code DD is diverted to the HSA, so they print no code W even though contributions are made to the HSA.
However, this does not appear to be sanctioned by the IRS - the W-2 instructions, for example, make no mention of this process.
So ask them if they are doing a "passthrough" and if they aren't tell them they need to issue a corrected W-2 with a valid number for code W in box 12.
In this case, it's not bureaucratic nonsense, it's that employers don't read the IRS instructions and/or don't understand them. The W-2 Instructions (line above) are written for the employer to tell them how to complete the form, not for the taxpayer.
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