You don't have to rip out the 1x6 subfloor planks.

Assuming you are going to tile the floor: You need 3/4" CDX (grade C top side / grade D bottom side / X exterior glue) screwed to the subfloor. On top of that trowel on thinset and screw down 1/4" cement board.

What are you planning to use under the tile?

Tile is usually placed on an underlayment layer rather than a subfloor so your question is confusing. If you are concerned about water damage add a layer of DITRA over the underlayment. Otherwise, a thin layer of cement backerboard is a good tile underlayment.

Your subfloor should not be getting wet.

I agree that the subfloor should not get wet enough, long enough to cause rot. If the old subfloor is intact there is the proof that it is not an issue.

If you take the contractor's advice and substitute plywood with waterproof glue it will, at best, rot as fast as the old boards, perhaps faster. To extend the life of the subfloor in constant contact with water you would need to use pressure preservative treated plywood. But that much water would destroy the ceiling below long before rotting any wood.

IMO your contractor is imagining a problem that doesn't exist. As I said, if you think the floor will be frequently exposed to a lot of water you should use a Ditra membrane directly under the tile and tub and keep a mop and bucket handy or consider a floor drain. I can think of no reason to alter the subfloor if it is structurally sound.

"pressure preservative treated plywood"

Will not rot but unfortunately it will delaminate if constantly wet

A properly designed and executed bathroom will not ever have a wet subfloor, or walls, or anything else. If your contractor is telling you up front that there is an issue with the subfloor potentially getting wet, then you know not to use that contractor!

Thanks for all the input. I might not have been clear enough in my original post. The 1 x 6 planks, though intact, are pretty old and there is a little bit of rot around the toilet. This house is more than 60 years old. The plumber is just concerned that the joint esp. between the tub and the finish floor, no matter how you seal it, will allow some moisture to escape through and cause damage to the already old plank subfloor below, which might fail under the weight of the new tub. We were considering an underpayment on top of the subfloor and putting linoleum over it. This is actually the reason I was hoping to put the tub directly on the subfloor so that the thickness of the underlayment will cover the joint at the bottom of the tub since linoleum is not thick enough by itself. My intent in the original question was to "reinforce" the old subfloor using a thin layer of exposure 1 grade plywood and set the tub as well as the underlayment for the linoleum on top of that.