As everyone else out here was so keen to spot, YOU do not know what the H-E-double toothpicks you are talking about - even if you are ex-military.
A reservist can be called up, even if they are part of the non-drilling inactive reserves. The key word here is RESERVES. Active reserves, inactive reserves...all available for recall. When you hear about veterans being called to active duty, that means the people who are no longer part of any reserves or are on the retired list. VERY RARE when it happens, but it does. The last time I recall veteran's being called back into service was back in the 80's when they took the battleships out of mothballs and made them active ships again. The Navy did a VOLUNTARY recall for gunner's mates so the old vets could teach the young sprouts how to maintain and fire the 16 inch guns.
If you are in the inactive reserve, yes...you do not drill, but you damn sure are available for recall!
Oh yeah...retired Navy speaking here, so I do know a little about this subject.