What Martha Stewart did was lie to authorities during the course of a formal investigation in an attempt to convince them that she did nothing wrong and end the investigation. That's completely and entirely different. It's also, by the way, the reason you should never speak to authorities, especially if you are the subject of the investigation. Exercise your right to silence. She chose to speak up and lied. If she kept her mouth shut she might have been able to escape prosecution. Anytime you open your mouth to authorities you open yourself up to one of these obstruction charges. The easiest solution is to just not cooperate one iota with them. Because as soon as you stop playing ball and doing what they want, they will try to use any one of the gazillion laws on the books to try and screw you. Not saying Martha is/was innocent. That's just my take on how I view a person's options when in that situation.
Obstruction charges usually stem from providing false testimony or evidence, tampering with evidence, or witness tampering. None of those, nor any related actions, are applicable here.