Kitchen tile on pier & beam
I have a pier-and-beam house, and the instructions are pretty much correct.

Tile will crack eventually when placed over pier-and-beam because of two related issues:


Floor joists often aren't on 12- or 16-inch centers, so they allow too much "give" when you step on the floor between the joists.
The piers are settling independently of one another based on soil conditions, and even fractional-inch movement is enough to crack grout lines over time.


So, if you really want tile, I would suggest removing the existing linoleum, then do the following:


Ensure that the subfloor is as level as possible before you begini. This is a lot better than to discover later that you need to shim your subfloor, use self-leveling compound, etc. for the tile to lay flat.
Lay a first layer of 3/4" plywood (or leave the one you have if it is in good condition and screwed down well).
Install a second layer of either 3/4" plywood or cement board going the other direction, so any movement at the first-layer joints is distributed across the second layer. Be sure to use long wood screws that go through both layers and back into the joists.
Install a decoupling membrane such as DITRA over the subfloor.
Install the tile.