The notion that you get prion diseases like BSE only by consumption of brain is not correct. Any part of the infected animal that contains nervous system tissue or lymphatic tissue can be infectious, although I guess this is dose-related.
Quote from OIE, "BSE. General disease information sheet" ([1]):
> The risk linked with consumption is addressed by the requirement for routine removal of all visible nervous and lymphatic tissue (Specified Risk Materials (SRMs)) from carcasses during the processing of cattle as well as the removal of any suspect animals from the human food chain.
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> Appropriate handling of nervous and lymphatic tissue tissues from BSE-suspect animals in abattoirs and laboratories is indicated to avoid accidental exposure (ocular or oronasal). Milk and milk products are considered safe.
[1] <
The OIE is the animal equivalent of the WHO.