Re Price Matching: You're both right.
It is correct that, in the US, insurance carriers must file their rates with individual states for the coverages those states require to be filed. Personal auto and Homeowners coverage are two that are almost always regulated, but the individual regulations depend on the state. The purpose of these regulations is to protect the Average Joe from the Big Bad Insurance Company.
However, there's also almost always some "wiggle room" allowed in the filed rates. Something like "+/- 10% factor may be applied based on risk characteristics not otherwise addressed". So, for example, if you told your insurance company that you biked everywhere and only drove your car 1,000 miles/year, where the rating model assumes 15,000 miles/year, they could use that factor to adjust the premium. However, they may not do that if there was already a "low mileage" credit applied. And they can only do this where the rate plan approved by the state allows for things like this.
Like most other businesses, insurance companies want new customers. They understand that things are competitive and will make adjustments in pricing to the extent that they're legally allowed to if you ask.
BUT, if you live in a state that has very strict regulations, it's possible that they didn't approve a "wiggle room" factor like that (or possible that the insurance company decided not to try to file something like that because it's a PITA to file those things). In that case, calling up might get your agent re-examine your file for anything you qualify for that you're not already getting, or they may say something like "well, I can't do anything with the coverage you have, but you're paying $100/year for roadside assistance. Do you need that if you're not driving much?"
Source: I work for an insurance company. Part of my job is working with the legal requirements and state filings, although my focus is commercial insurance.