Time for some straight talk from someone who is immersed in the Fremont market - first of, an answer to your first question:
Q: How important is termite disclosure in deciding whether to buy a house?
A: VERY. Be grateful that the seller was kind enough to provide a report up front. You will know BEFORE you write an offer what the issues are, not find out once you are in escrow like many other properties. You want a termite report for every home you plan on buying - whether it's provided up front or once you get into escrow.
Here are some important tings to consider:
(1) First of all, termites are VERY common in Fremont. If a home doesn't have them yet, it will. The trick is to stay on top of them and understand what you are looking at when you look at a report. Your agent should be helping you decipher the report. Termites in and of themselves should not be a concern.
(2) Just because it says "Termite Report" does not mean that everything reported in it will pertain to termites. Termite Reports are subdivided into 4 categories - Section 1 - anything that has actually damaged the wood structure of the home, Section 2 - anything which, if left un-repaired, could lead to Section 1 damage, Section 3 - "Further Inspection and Section 4 - "Other."
Section 1 is what you are most concerned about and not everything in Section 1 will be concerning termites (or wood-boring beetles). Fungus also attacks wood and, in my opinion, is most often a worse issue than the insect damage. ALL Section 1 damage CAN be repaired - it's just a matter of how much it will cost.
(3) The market in Fremont is beyond HOT - if you want the house in Fremont, It WILL be "AS-IS" and you will more than likely be paying over asking regardless of the condition. The fact that someone below suggested you can take the cost of repairs off the price is simply not going to happen. Someone else suggested that you could ask for a Section 1 clearance - again, not going to happen
(4) They have provided you the report up front as a courtesy so you know what you are getting in to when write your offer. Once you get into escrow, I recommend you also order your own set of inspections: Termite, Property, Roof AND chimney. Just because a chimney is shaking when a person grabs it and shakes it does NOT mean it will fall down or is damaged. It should probably be braced, but that is true of most masonry chimneys. The chimney inspector will be able to tell you what is up. Most chimneys can be repaired if they have problems. Again, it's an issue of how much will the repairs be.
(5) There are some strange answers below, but Elva's response is spot on: if termites are only in one location, you deal with them where they are. If their actual location cannot be determined, then you treat the whole house - typically by tenting and pumping in Vikane gas. If you don't need to treat the whole house, don't. Talk to the inspector to get their recommendation - this is what they do for a living. They will not insist on a whole house treatment if you don't need one. Once you are moved in, get frequent inspections to stay on top of things.
(6) If you pass on this house, remember that you will encounter termite report issues again. The issue is not termites or dry rot - it's how much it will cost to remedy the issues when you treat them. Over the years you live there, provide preventative maintenance so it won't be an issue down the road.