From the Interval documentation:

For approximate machine- or arbitrary-precision numbers x, Interval[x] yields an interval reflecting the uncertainty in x.

$Version
(* 10.4.0 for Microsoft Windows (64-bit) (February 26, 2016) *)

Interval @ $MaxNumber === Uncompress @ Compress @ Interval @ $MaxNumber
(* True *)

IntervalMemberQ[Interval @ $MaxNumber, $MaxNumber]
(* True *)

IntervalMemberQ[Uncompress @ Compress @ Interval @ $MaxNumber, $MaxNumber]
(* False *)

What is going on here? What happens with the interval after the compress-uncompress round-trip?