I really don't get her point as Kerry has always made it clear that he coordinates with her - when he could speak of coordinating with the Obama administration or even Obama without overstepping. He seems very sensitive to her defensiveness.
All I can think of is that these 4 things might be part of it:
1) Remember how she completely overreacted to the question about Bill Clinton's position from the young African guy? That REALLY was mishandled.
2) Remember the comments of her rolling her eyes and blasting Kerry to Levin, Reid and others for introducing Kerry/Feingold?
3) Remember the Clinton team spreading the story that Kerry was not picked for SOS because he was "weak"?
4) Remember the bizarre puff piece that came out where Hillary was touted as the point person for Afghanistan and even credited with his decision for the runoff - saying she bonded via her own campaign's experiences - using almost the same words used a few weeks before in descriptions of Kerry's trip?
I suspect that HRC is still not really over not getting the nomination. Her Secretary of State position did give her a second chance to be a really significant player - and she is. But, unlike Kerry, who also lost the possibility of being President, she really does not seem comfortable with herself and her life - resulting in her snippy comments here and in Africa - maybe both in relationship to not feeling she is getting enough respect.
It is possible that Kerry never was someone she particularly respected or liked even before he endorsed Obama. One little story in a book by Sid Blumemthal of his years with the Clintons spoke of what might have been their first major interaction. Kerry, along with Bradley and Moynahan and possibly a few other Senators came to Clintons very early in his Presidency and advised that they simply put out everything there was to put out on Whitewater and cut the distraction in the bud. From Blumenthal's description, Hillary went ballistic after they left ranting that people were against them.
It may be Clinton's neediness that is the problem. She really has not had many diplomatic triumphs as SOS. Obama is the one who has set the tone - something few Presidents would not do. The problem might be not just that someone else has capably handled many of the biggest problems. If it were Holbrooke or Mitchell, I think she would be fine and see it as a credit to the "team". with most negotiations, it seems that career foreign policy people do most of the ground work. I suspect it is because it is Kerry, who is not one of the nameless, to most people, officials. It likely bothers her that in all the cases where Kerry intervened he was better positioned than she was - even though she is the Secretary of State.
I had an interesting conversation with my brother in law whose company worked with US AID. He really thinks her real legacy will be the changes made to how the state department runs. Now, we know that Kerry and Lugar proposed many of those changes before she was in office more than one month, but, it will clearly have been Clinton who implemented them. I suspect, that if she were not Mrs Bill Clinton, that would be something that she would be incredibly proud of and it would be enough. I suspect that she resents Kerry getting the credit he does. Might be she resents the fact that some might think that he would have been a better Secretary of State.
As to the last paragraph, it is a rewrite of history. Kerry made the connection with Assad and lobbied for an Ambassadorship for Syria and he spoke of the HOPE or the POSSIBILITY that Syria could be moved to break away from Iran. He never called him a reformer, he called on him to reform. The one who called Assad a reformer was .... Hillary - and the world's media picked it up. (Here's one example -
http://www.israelnationalnews.com/News/News.aspx/143161 ) This really was a high level gaffe and her attributing to Congressmen of both parties is just wrong. I suspect that this was one of the sources for the ramp up of the Kerrys were BFF with the Assads story that you alluded to. (The Clinton links are easy to find - I tried a comparble Kerry Assad reformer and none in the first few pages have Kerry calling him a reformer.)