'Money's not as valuable to our organization as knowing who to trust'.
I don't think Le Chiffre was cooperating with EITHER Vesper or White at this point. She could have passed on the information about 'the tell' to White who could have passed it on to Le Chiffre. We don't know if she had any contact with Le Chiffre. We know Vesper was cooperating with White. The final word on whether Bond would be given a second chance to buy in fell with Vesper, not M. Mi6 requested the funds, and was given the green light to tap into the treasury for the operation - with Vesper being appointed to the role (with help from Quantum, probably) of guarding the Treasury's money from being frivolously spent by Mi6 in a way that would directly finance terrorism. Bond could not bypass her by going directly to M for the money, because the money belonged to the Treasury, NOT to Mi6.
