Since the reform and opening up, people's payment methods have undergone tremendous changes. In recent years, mobile payment has become one of the main payment methods. To understand the usage of two mobile payment methods, $A$ and $B$, among students at a certain school last month, 100 students were randomly selected from the entire school. It was found that 5 people in the sample used neither method. The distribution of payment amounts for students in the sample who used only method $A$ and only method $B$ is as follows:

\begin{center}
\begin{tabular}{ | c | c | c | c | }
\hline
Payment Amount (yuan) & $( 0,1000 ]$ & $( 1000,2000 ]$ & Greater than 2000 \\
\hline
Payment Method &  &  &  \\
\hline
Using only $A$ & 18 people & 9 people & 3 people \\
\hline
\end{tabular}
\end{center}

(I) Randomly select 1 student from the entire school. Estimate the probability that this student used both payment methods $A$ and $B$ last month;
(II) Randomly select 1 student each from the sample students who used only $A$ and only $B$. Let $X$ denote the number of people among these 2 people whose payment amount last month exceeded 1000 yuan. Find the probability distribution and mathematical expectation of $X$;
(III) It is known that the payment methods of sample students did not change this month. Now, 3 students are randomly selected from the sample students who used only method $A$, and it is found that their payment amounts this month all exceeded 2000 yuan. Based on the sampling results, can we conclude that the number of students using only method $A$ in the sample whose payment amount this month exceeded 2000 yuan has changed? Explain the reasoning.