Depending upon how the television company came across your photo, they may have no idea whether you are a professional who expects to receive good money for your work, an amateur who lucked into a really nice photo and would be delighted just to see his work on television, or something in-between. Further, while it's possible that your photo was uniquely suitable for their intended usage, it's also possible that they might have a stock library with a pre-paid license that contains a photo which they could use, but that an employee of the station happened to see your photo and thought it was better.
If the television company had a library photo they could use, but a better photo was available from someone who would be happy just to see it on television (possibly with "Photo courtesy of XXX YYY" in the corner), use of the better photo would represent a win-win both for the company and for the photographer. I would think that seeking to license the photo for $1 may come across less well than seeking to license in exchange for an on-screen photo credit and then, if the offer is accepted, arrange for a $1 payment "because legal insists upon it". Even people who would be happy to volunteer something for free may be insulted by what's seen as a low-ball purchase offer, so delaying the notion of payment until the offer is accepted would seem like a good idea.
With regard to budget, it's possible that the station's "budget" for the photo was already spent on a pre-paid stock image license; the maximum amount that can be spent on an alternate image may depend more upon the corporate environment than upon the value of the photo in question. Many corporations allow lower-level employees the authority to make small purchases at their own discretion, but require higher-level approval for larger purchases. If higher management would balk at the idea of paying anything for a photo to fill a spot where it could use a photo that's already paid for, the maximum payment the company could offer would be limited to the lower-level employee's discretionary spending authority.
In short, I wouldn't interpret the $1 or $50 offers as insults, nor an effort at the company to "cheap out" on background artwork, but would more likely represent a situation where the company had a licensed library of background art available, but would prefer when possible to give other photographers who would like to have their work shown on television a chance to achieve that. Based on what you've written, I see no reason you should feel insulted by the offer. Instead, you should recognize that when a potential buyer to values something far less than a potential seller, that doesn't doesn't imply that the buyer or seller is "wrong"; it merely means that buyer and seller are not a good match for each other. It's entirely possible that the buyer might find someone else who would supply something even more suitable to the buyer's needs at a lower price, and that the seller might a buyer who would be happy to pay even more than the seller had been asking.
Note also that while the market for professionally-taken pictures might be slightly diluted when a amateurs who luck into the perfect combination of lighting and composition give his work away for practically nothing, there may not be any realistic way for amateurs who luck into such pictures to receive for them anything near what they could receive on the professional-photography market. People who are looking for pictures that would be worth $5,000 are apt to spend more of their time looking at pictures in that price range than at pictures which could be had for almost nothing. If improvements in image searching tools make it easier for unusually-good pictures by amateurs to get noticed by people willing to spend real money, then the market could be diluted by amateurs who were still willing to give away pictures for free, but the improved level of notice would make it easier for amateurs to demand more money.
PS--if you don't want to receive purchase or licensing offers below a certain amount, you could include such a statement on your on-line pictures. If you watermark your pictures with a notice: "Licensing offers below $250 will not be considered", then people who might have sought to license them for less than that can avoid wasting their time and yours.