As I see it Ti is a filter for the information we receive, Ti takes the idea or information and analyzes it with skepticism comparing it with what we already know is truth so that we see if the new information fits the framework or not, it also analyzes it with pure logic, finding if the new idea/information contradicts itself or contradicts another axiom of logic.Introverted ThinkingAnalyzing; categorizing; evaluating according to principles and whether something fits the framework or model; figuring out the principles on which something works; checking for inconsistencies; clarifying definitions to get more precision.
But when a self proclaimed INTP is too stupid(lacking the intelligence to apply logic) or too ignorant (not having the means to compare the new information with previous known knowledge) to analyze something properly, then it's as if he didn't have Ti in the first place.
He may receive the information and accept it without doubting it for a second eliminating the purpose of Ti as a filter.
Then it doesn't matter if someone has the tendency to analyze everything, if there's no intelligence and knowledge, Ti doesn't work.
That's why Intelligence and Knowledge is a requirement for INTPs and no INTP can exist without it.