She is absolutely using bad faith here because DEPRESSION IS CAUSED BY DYSPHORIA
Dapression is ALSO caused by a myriad other things than dysphoria.
You are assuming that if a child presents with depression and also claims to be transgender, then the transgender MUST BE THE ONLY POSSIBLE cause of their depression - even if the depression predates any indication of dysphoria whatsoever.
When there is both dysphoria and depression, some of the depression WILL BE caused by the dysphoria.
It is certainly not the only cause but where there is dysphoria, it always deserves immediate evaluation.
If there is less depression after solving the dysphoria issue, then we can keep on treating that, but if the depression is caused by dysphoria, it will not be resolved no matter what other things you try.
If treating for dysphoria has no effect on the depression, and the evaluation indicates that their dysphoria is based not on solid footing and motives, it can be terminated with no major complications especially in a 6 week time frame, but the same cannot be said the other way around, especially in the case where a voice suddenly changes, or breasts develop.
If that happens in those six weeks, and there is genuine dysphoria, the dysphoria permanently gets WORSE and in fact becomes untreatable for years.
There's no good case to delay on an introduction of blockers, because it WILL make things worse for those with dysphoria and immediate treatment won't make things worse for those without.
Arguably, a few weeks' break from hormones will allow folks to contextualize their hormonal situation and effects anyway, and I think that's yet another benefit of doing so. Being able to observe when "it's the hormones" rather than "it's just me" has real value.