The wording of the contract might be either way but expectation should play a part as well. If you replaced the tub,bath sink and kitchen sink,without a doubt everything between sinks/tub and below floor should be new including not only drain pipes but also water supplys, angle stops,strainer stoppers,diverters and facuets. If you replaced cabinets and vanity but not sinks and tub,I would certainly think upgrade would include afore mentioned. The statment about upgrading tub plumbing is imo reason to believe all the pipes were being replaced. I don't know if that answers you question but if you are only asking about the $300 additional for the drain pipe in kitchen,that sounds over priced. More important,unless there were prevision for over runs,it doesn't sound like you aurthurized added cost as should have been before work was done.
Is he correct that I should have specified that I want all the plumbing and the drain pipe to be replaced? NO, he is not correct. Upgrade all the plumbing covered it all so you didn't fail to specify what was to be replaced.

Yes, I am replacing everything (tub, cabinets, sink, etc) in each room. I also explained to him before I hired him that I eventually wanted to replace all my plumbing since it is falling apart and I recently had to fix a bad leak and replace a section of my drain pipe underneath the house. So I told him to replace all the plumbing in the walls for the sinks and the tub so that I don't have to reopen the walls when I upgrade the plumbing under the house.

Hopfuly others weigh in but I don't know why anyone would reinstall used material from sink to wall.

He didn't reinstall the used drain pipe from the wall to the sink. The dispute is regarding the drain pipe in the wall (from the crawl space up to the cabinet).

Interesting
""upgrade all of the plumbing in the sink and the bathtub from below the floor, up"

Excluding the mechanism and finish hdw, the tub waste and overflow are a "T", a couple pieces of pipe and a nut or two and are integral. While parts are above the floor, they are part of the drain system, which are connected at a trap.
Under the pullman or lavatory, any fitting "after" the trap is considered part of the drain system.

So, he's shot himself in the foot;"from" below the floor, up"

This;"from below the floor, up", removes the "unforeseen" clause found in most contracts, which is often used by shysters, charlatans and uninformed salesman, as a method of CYA monetary extraction.

The fact that he is employing these tactics tells me that he's found something which may affect his product warranty.

Although verbabl contracts are valid,they make it more difficult to to settle disputes. If you have a writen contract with the words you put in quotation,as snoonyb said, he is trying to whoo-doodle you big time. I'm not sure us telling you that changes anything.

Historically, plumbing in a residence has included two separate systems, Supply and DWV. The two are never cross connected. Sounds as if an unknowing homeowner has been victimized by a lack of knowledge.

If this comes down too the contractor attempting to take the easy way out and not wanting to explain to you the conditions which cause him concern or that he's underbid the project, there are a couple of steps to take as a process of elimination.

Since you say that you had indicated that you were going to replace the or have repairs to the "beneath the floor" drain system, wouldn't come as a surprise that a couple of plumbing co's give you estimates or that you obtain standard fumapest reports.