Step 1: Set the background.
Noble gases were once thought to form no compounds. The first noble gas compound came from a clever observation by Neil Bartlett.
Step 2: Read Statement I.
Bartlett saw that platinum hexafluoride could pull an electron from oxygen to form the salt $[O_2]^+[PtF_6]^-$. \[ O_2 + PtF_6 \rightarrow [O_2]^+[PtF_6]^- \] This idea led him to try the same with xenon.
Step 3: Judge Statement I.
Because this reaction inspired the making of xenon fluorides, Statement I is correct.
Step 4: Read Statement II.
Bartlett's reasoning worked only because the first ionisation enthalpy of $O_2$ is very close to that of xenon.
Step 5: Judge Statement II.
The first ionisation enthalpy of $O_2$ (about 1175 kJ/mol) is nearly the same as that of Xe (about 1170 kJ/mol). So Statement II is also correct, and it explains Statement I.
Step 6: Combine the judgements.
Both statements are correct, and the second one supports the first.
Step 7: State the final answer.
The correct choice is:
\[ \boxed{\text{Both Statements I and II are correct}} \]