The best advice I can give anyone when dealing with Date/Time issues is to remember that a "date" (or a "time") is an abstract moment in space/time ... it doesn't matter whether you are in California, or Indiana; it doesn't matter if you observe Daylight Savings time or not; that moment is the same all over the galaxy.
When you describe that moment in text, or in speech, your description inherently takes into account a "base moment" -- just as if you were describing a physical location and you said it was "20 feet up, and 30 feet west", there is some implicit orrigin in your coordinate space that you are speaking relative to.
When you write the text "June 5th, 2003 at 9:36AM" you are describing a moment in time that assumes:
- A Specific type of Calender
- A Base moment that caledner starts at
- the length of a second/minute/etc..
Many of these things are accepted by convention. people assume you are using the Gregorian calender unless you tell them otherwise, they assume you are using standard month names, and standard lengths of a "second" .. but what they don't know is what origin you are using, and what time zone you are using ... that information should be spelled out in your expression of the moment in time as a string.
In your specific case, I would want the API provided to me by the other servers I deal with to make sure that the time is expressed in a format that includes the TimeZone, so I could know without a doubt what they mean.