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There are few major disclaimers on the above.

Disclaimer 1

Pressure Speed Statement does not mean that pressure dynamics in one well is totally synchronised with 

Disclaimer 2

The fluid flow in porous media only starts above a certain pressure gradient threshold.

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In practical terms this effect can only be captured at very high distances between wells or at regular cross-well distances but in low mobility formations ( usually low permeability and / or high viscosity oil ).

Disclaimer 3

The actual physical process behind pressure diffusion  in porous media is density impulse transport which propagates at speed of sound in fluid-filled porous rocks (thousands of m/s ).

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That totally justifies describing the pressure dynamics with diffusion equation.

Disclaimer 4

The actual reservoir where pressure dynamic is studied is not an isolated physical object.

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