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Isn't the MIDI spec limited to around 1ms per MIDI event?
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That's correct - due to the serial nature of MIDI, the more MIDI events you have going on, the more likely it is that timing accuracy will get worse. You can alleviate some of that by getting a MIDI interface that supports time-stamping with the audio application you're using (currently, only the MIDI IO will do this with Pro Tools).
While time-stamping can improve MIDI timing, it's not a catch-all. Any time you're sending a lot of MIDI data down a cable, it's going to decrease accuracy. All that time-stamping does is 'pre-cache' the MIDI data at the MIDI interface so that it can then be transmitted more accurately. Without time-stamping, MIDI events are tied to the computer clock - which, if it gets busy doing other things, can cause some timing inaccuracies. While time-stamping can improve accuracy between the computer and the MIDI interface, it cannot overcome the inherent limits on transmission speeds between the MIDI interface and your device, or your devices accuracy when playing back incoming MIDI data.
The best way to keep timing accurate is to limit the amount of MIDI data that any particular device is receiving at any one time. Filtering any non-essential messages can improve timing quite considerably.