Think of the hiring process as a sales experience, where you are the product being sold (not literally of course). Potential employers are customers interested in buying the product. Some need more functionality (capabilities), some need less. If a customer needs less, they are likely to realize they don't need to pay for a fully-featured product when they can get a discount product that does what they need, though perhaps not quite as effectively.
This is all about supply and demand. If you're a highly-skilled employee (experience is an indication of this - nobody actually hires for what you've done in the past), then you're the Cadillac of products. You aren't going to be cheap, and they know that. If they're looking a discount it makes sense that they'll go elsewhere.
Headhunters / staffing agencies are akin to them bringing in a personal buyer for the product they're interested in (similar to a realtor). They often know the marketplace and what things cost, and are already set up to aid in connecting a buyer and seller. If a customer brings in a buyer, I typically think it's a good thing because it means they are serious about getting the right fit. You and your customer (future employer) may be able to find each other on your own, which may save the customer a little money, but that is more rare than finding the right customer with professional help.
This metaphor also helps when thinking about price (salary) negotiations. You want to make sure you're in the right ballpark with regard to buyer and seller pricepoints fairly early on. On the other hand, you want to not lock yourself in to a particular price until you've had a chance to really understand each other and negotiate.