What your contractors are bidding is common practice in San Jose. "Chicken wire" AKA 20 gauge 1" mesh is the preferred lath of choice for bay area tilemen. It is 100% up to the job as long as it is galvanized and self-furring.
I am going to talk about the "one-coat" mortar bed method later in this post, both for your and "in-general" information for those here that wonder what the difference may be.
San Jose is one of the few municipalities in the bay area Which does not
require interior lath inspection. This does not mean that common practices as required by the other municipalities that do require inspection may be ignored.
Ask the bidders "will you be following the interior lath requirements of Los Altos, Cupertino, Campbell, Los Gatos, Saratoga, Sunnyvale, (....etc) when you lath my shower?" The general guidelines are:
1) Minimum water-resistent ("green") drywall, but most now call for Denshield in wet areas. If your contractor will be replacing the drywall, tell him you want Denshield in the bid.
2) Waterproof paper; 30-30-30 Kraft paper (Aquabar, Rattan, etc) or 15 lb roofing felt or better. Paper run horizontal, starting at the bottom, ship-lapped min. 4", no tearing. Minimum vertical overlaps 12".
3) Galvanized self-furring metal lath, 20 gauge minimum woven mesh (chicken wire) or 1" self-fur welded-wire 18 gauge are normal. 3" minimum overlap regardless of type of lath.
"Diamond", or expanded lath is not common for one-coat, but some use it. If the guy wants to use it, it must be furred
(which is why almost nobody uses it for one-coat).
4) Mechanical attachment. Lath to be nailed-off using 1 1/4" (min) galvanized "roofing" nails or equivalent 1 1/2" roofing staples 6" OC (on center) all studs max 16" OC. No nails @ inside corners. Nails at lath overlaps. Non- self-furring wire requires furring nails (which is why everybody uses self-furring wire).
So, as a layering: drywall/denshield, waterproof paper, metal lath, mechanical attachment. The purpose of the drywall/ is as a backer for the mortar bed. The HD guy was actually right about that.
The California bay area is in a high earthquake zone. Statistics have shown that the "one-coat" mortar bed method fairs better than any other tile installation method including non-mortar bed (cement backer-board etc) in sever earthquakes
. Most of this information, along with countless changes to structural requirements for 2-story or less residential structures came following the 1989 Loma Prieta earthquake, a 7.1. (side note: I wish I had bought Simpson Strong-tie stock in '88 LOL!). The rest of the country would be amazed at what our framing looks like here in CA, or our concrete foundations. My house, built in 2003, is on a "post-tension slab foundation". It is 12" thick, and has thick/sheathed steel cables 12" OC both directions. A couple weeks after the slab is poured, tension is applied to each cable in the thousands of pounds per square inch, then capped and welded. They do not crack, and crack-isolation membranes for this type of slab are optional but not needed.
Back to tile on walls in an earthquake: why is one-coat best? Very simple:
1) At 1/2" thick, the mortar bed has a lot of flexibility ie it can bend without fracturing. As the mortar wraps a corner, there is equal strength. As there are no panel seams in which strength is lost, the entire mortar bed is a single monoque structure without inherent weak points.
2) Furred lath means that the mortar has completely wrapped the wire. The wire is well-embeded in the mortar, and thus will not let-go of the mortar. Mechanical attachment means the lath will not let go of the wall structure. Directly at the attachment point, the lath can bend under stress without letting go of the nail. Nails cannot "pop" like on sheet goods (drywall, cement backer board, etc).
3) The waterproof paper is dual function. It also serves as a cleavage membrane.
The mortar bed can in effect "slip" on the drywall beneath, moving with the ground movement and lessening fracture. Thus no nails in the corners. Hmmm...
This is why they fair better than any other installation method.
These are not my ideas. This is what the building inspectors say when they are asked "why?".
After the Loma Prieta quake, studies were done. All of a sudden, everybody's building dept. wants to see paper and nails. They are less concerned about mold/rot than about slabs of tiled walls falling on people. Luckily, waterproof paper serves both
Regional practices are important
. I know I would want a house built to withstand hurricanes where those happen. Not sure what withstands tornados (gulp). But I'm very sure I want a house that I don't have to be dug out from under here in earthquake land.
The bids sound typical to me. Mortar bed shower (wet area), thin set wainscot (dry area), and thin set to slab floor tile. However, if you are not on a post-tension slab, tell them you want a crack isolation or anti-fracture type install on the concrete. Or Laticrete CST (or equivalent) thin set used. That should not add much to the bid.
Good luck, and show us photos so I can see what my competition is up to