The scene is apparently humor based on a non sequitur response to an idiom. It's obviously contrived just for the scene.
Lori's sentence is in two registers. To be in the same register, she'd have to say "Ted's a fox" or "Ted's a real hunk" etc.
She used the word "snatch" to mean "catch" or "land" (as in secures as a boyfriend or husband), as a fisherman catches and then lands a fish. Tami-Lynn is trailer trash, so her mind is in the gutter, which is why she'd think of the obscene term for female genitals when she hears the word snatch. She's not overreacting, just showing her deplorable vulgarity.
This is akin to what happened in 1999 in Washington, DC, when David Howard, an aide to the mayor of DC, used the word niggardly about a meager budget, but some lexically and linguistically ignorant African American thought it was an ethnic slur (the N-word) and made a big pointless fuss about it. Howard resigned his job because of it.
The point is that person A says X, which means 123, but person B mistakenly thinks it means 666, so a miscommunication occurs. Of course, because it has to do with sex in TED, the writer thinks he's being clever, but he's really only pandering to the junior high school reptilian brain of most of the audience.
Homonyms are a source of humor in all languages. Some are clever, but most are adolescent or base, somewhat like Tami-Lynn.