Let me synthesize and elaborate on Catsmine and MsCanFix's response.
There are three main types of termites feasting on homes in the United States - drywood termites, dampwood termites, and subterannean termites. An inspector should be able to tell you which species you have, ideally, but not always, by scientific name.
Their lifestyles differ in that subterannean and dampwood termites nest in the ground or in moist wood. Foragers bring food back to the nest and queen who live underground. If you can break the soil to house contact by creating a chemical or sand barrier, then you can treat your house at a much cheaper cost, than the whole house treatment outlined below. Whole house fumigations are not used to control subterannean and dampwood termites. These types of termites are treated by barrier placement of insecticides like Termidor or baiting programs with Sentricon. The basement location of your termites might indicate subteranneans...
Drywood termites can nest in your house and do not need soil contact to reproduce. There are bascially two methods to treat a home for drywood termites - whole house fumigation and spot treatments. Because termites live in difficult to inspect areas, a whole house fumigation, when properly done, is the only complete way to guarantee that termites have been eradicated. A whole house fumigation involves covering the entire house and injecting Vikane gas into the living space of the house, usually over a period of 2 days. You are required to remove all your opened food items, and vacate your home for that time. As you can imagine this is an expensive, much more than $350, and bothersome operation. Some people object to the use of the gas. Heat can also be used to conduct a whole house fumigation.
A spot treatment works only where they place the chemical, heat, microwave, electro-gun, or liquid nitrogen freeze treatment, and sometimes it doesn't work that well. It is highly dependent on finding the infestation, and treating it properly. If you have a small infestation then spot treatments are legitimate.
I think it is time to request a new inspection from a different company or two. Do not give them any clue about the previous inspection. Let them come to their own conclusion on price, location of infestation, method, and species ID. If the inspector does not know what he/she is talking about or disses you in any way, don't hire that company.
In my state of California, there are two types of companies - companies that have the capability to conduct whole house fumigations, and are either main contractors or sub contractors; or companies that mainly do general pest control, can inspect for termites, but contract the fumigation to a subcontractor. I am not sure how this might affect the price, but it probably has some effect.
Termite Management Guidelines--UC IPM
Drywood Termite Management Guidelines--UC IPM