The story...

A change in standard operating procedures [for fighter intercepts] was introduced on June 1st, 2001; this inserted the Secretary for Defense into the bureaucratic chain. This marked a radical departure from procedures which had been in successful operation for some 35 years. Now, the approval of the Secretary of Defense was required for the scrambling of aircraft... The authors of this change may have been seeking to introduce that element of disorder and uncertainty which might be necessary in order to allow the success of the upcoming operation.
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9/11 Synthetic Terror: Made in USA
Webster Tarpley

Our take...

You’ll see this claim spelled out in a number of places. Here’s what 911research have to say:

The June 1 Order
Intercept Authority Was Restricted 3 Months Prior to the Attack

Prior to June, 2001, commanders of domestic Air Force and Air National Guard forces enjoyed considerable autonomy in ordering intercepts of errant aircraft. We know that interceptors were scrambled frequently to persue and investigate civilian aircraft that had deviated from their flight plans or were unresponsive.

On June 1, 2001, S.A. Fry, Vice Admiral of the US Navy and Director of the Joint Staff, issued Chairman of the Joint Chiefs of Staff Instruction CJCSI 3610.01A [cached], profoundly changingd intercept procedures. It required that all requests for asistance in hijackings be approved by the Secretary of Defense. The order states:

In the event of a hijacking, the NMCC will be notified by the most expeditious means by the FAA. The NMCC will, with the exception of immediate responses as authorized by reference D, forward requests for DOD assistance to the Secretary of Defense for approval. 

Reference D refers to Department of Defense Directive 3025.15, dated February 18, 1997. That directive allows commanders in the field to provide assistance in emergency situations to save lives, but any requests for "potentially lethal support" still require authorization by the Secretary of Defense.
http://911research.wtc7.net/planes/defense/june1.html

Sounds compelling, but perhaps that’s because you’re not seeing the full picture. In particular, what the earlier document said. So, here’s the wording of the July 1997 document:

In the event of a hijacking, the NMCC will be notified by the most expeditious means by the FAA. The NMCC will monitor the situation and forward all requests or proposals for DOD military assistance for aircraft piracy (hijacking) to the Secretary of Defense for approval.
http://www.dtic.mil/doctrine/jel/cjcsd/cjcsi/3610_01.pdf

And for easy comparison, the June 2001 document that “profoundly changed intercept procedures”:

In the event of a hijacking, the NMCC will be notified by the most expeditious means by the FAA. The NMCC will, with the exception of immediate responses as authorized by reference D, forward requests for DOD assistance to the Secretary of Defense for approval.
http://www.dtic.mil/doctrine/jel/cjcsd/cjcsi/3610_01a.pdf

So what’s changed?

#1, the statement that the NMCC “will monitor the situation” has been dropped. Seems odd, as it’s hard to believe they would do anything else, but in any event, as long as they deal with requests as they arrive then there’s no issue here.

#2, there’s a new exception of “immediate responses as authorized by reference D” (see the 911research quote) to this rule, therefore under some circumstances the new regulations require less approval than the old.

#3, Previously both “requests and proposals” for assistance required approval, now it’s “requests” only. Doesn’t seem to be a significant change.

#4, “DOD military assistance for aircraft piracy (hijacking)” is replaced by “DOD assistance”. This appears to do no more than remove a little redundancy, in that we already know from the beginning of the paragraph that this is about assistance for a hijacking. 

And, ah, that’s it, at least with this paragraph: no evidence here that the new regulations affected the 9/11 response, at all. 

We don’t think the other changes in the document would have done so, either (the paragraph we’ve highlighted is the one that gets all the attention), but for thoroughness we’d recommend you check both documents out for yourself. The 1997 version is at http://www.dtic.mil/doctrine/jel/cjcsd/cjcsi/3610_01.pdf , and the June 2001 version is at http://www.dtic.mil/doctrine/jel/cjcsd/cjcsi/3610_01a.pdf .