This is indeed ambiguous, for the reason you have highlighted. ‘Avoir les moyens’ is so commonly used to talk about financial affordability that using when talking about money almost imposes that meaning on it.
There might be an humorous effect in that sentence but no real ambiguity.
Avoir les moyens means to be able to, to have the capacity to achieve something, here the woman says she is not able to spend that much money, that it is beyond her capacities.
It is true avoir les moyens financiers is by far the most common implicit meaning but that’s not the only one. The factor can also be physical (il a les moyens de gagner la course), intellectual (il a les moyens de comprendre), popularity (il a les moyens de gagner l’élection), evidence (on n’a pas les moyens de le vérifier), etc.
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