Your agent is correct in that no other insurance company will want to insure your home while it's in a damaged, uninhabitable state. That said, this fact doesn't mean that other insurers would automatically turn you away once the repairs have been completed and the house has been deemed inhabitable by an inspector. A lot of factors come into play.
Other home insurance companies, for example, must determine if you are at risk for another fire or other self-caused accident. If you had even one previous claim for damage that occurred as the result of an accident on your part or the part of someone who lives in the home, other companies might consider you to be too much of a risk. If a company does decide to insure your home, you will likely face much higher premiums since you've already had one incident that caused your previous insurer to have to pay out a lot of money. Since insurers often change their policies, the best thing you can do is call other insurance companies now to find out their current and expected future policies in regards to homeowners in this type of situation.
You don't mention if your insurer agreed to pay for everything. If you're paying a lot out of pocket or perhaps they even rejected your claim, speak with a lawyer before accepting that they won't cover something like removal of toxic materials, repairing or replacing property and/or inspecting the site. These types of fires are fairly common, especially around the holidays, and insurers often cover at least one event. That said, some homeowners don't arrange enough coverage, which means that the insurer only has to cover what they agreed to in the policy and that amount might not be enough to deal with all of the damage and losses. Lastly, talk to your restoration specialist about the companies who they deal with who insure homeowners who previously had a grease fire. They deal with enough of these fires that they know which companies give homeowners a second chance.