I'm the IT Officer here at my FI, and there's no way I would allow this, and there's no reason that they should request it.
I'm not familiar with this company, but I wouldn't (and won't!) be doing any training or any business with them.
Their "advice" flies in the face of basic common sense and security procedures!
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"Gratitude makes sense of our past, brings peace for today, and creates a vision for tomorrow." - Melody Beattie