While I see where you're going with this, let's take a moment to remember that the Joint Terrorism Task Force is made up of individual law enforcement officers, not agencies. That is to say that not all members of the Whatever County Sheriff's Department are inherently part of the Joint Terrorism Task Force.

So it's certainly possible that three black SUVs worth of the local sheriff's deputies, all of whom were members of the Joint Terrorism Task Force, showed up to question her about her internet searching.

Or this fiction writer is not portraying an accurate version of the events.

Basically, it's a modern day "posse" made up of individuals from Federal law enforcement (FBI, Secret Service, ICE, Border Patrol, etc) and from local or specialized law enforcement (railroad police, etc).

The officers are basically deputized as JTTF members. It's a common model that's been around for a long time. For example, the US Marshalls have a fugitive task force for picking up suspects with arrest warrants and the DEA has something similar for drug raids.

According to David Gomez, a former FBI exec who worked in domestic terrorism, "JTTF" is a catchall term used by many (perhaps all) LEOs working on terrorism in any capacity. The term apparently has no technical meaning.