There were a number of things going on.  Remember the world was different.   First and foremost, was that IBM was so big and other large firms were getting out the business such as GE and Xerox.  As I understand it from my IBM friends that were there at the time was that IBM was concerned that the justice dept would go after them.  The amount of business Amdahl bleed off was small compared to what IBM was making, so I suspect that it played into any business decisions.

Amdahl legitimized a lot of IBM's practices and in many ways, and as the Harvard Business School teaches, "It is always better to have a small weak competitor than none at all."  At the time the price difference (certainly for universities) was huge.   I remember when CMU was making the decision to replace the IBM 360/67, IBM bid a 370/168 an Amdahl a 470/v7 and DEC a PDP-20 (DEC won).   IIRC: The difference in quotes between IBM and Amdahl was a factor of two.  DEC was cheaper still, although, in the end, CMU had to buy 2 of them to do what they had been doing with the 360 previously.

Also, remember the IBM OS's were published and thus all the sites had the full sources. It was built on-site for that specific installation and each site tended to have made small local mods.    PTF's (Program Temporary Fixes - aka patches) came out from IBM as the source and you applied the PTFs yourself (my memory was for most PFTs we had about a 2-3 month lag from recent from IBM before we had them in to the system).  But folks took the original code whole cloth and changed it too.   For instance, CMU took the TSS source which did not work (crashed every few hours) after a year or so, had fixed it to work reliably enough to be the system running on the 360/67 24/7.  On the other hand, U Mich took the TSS sources and rewrote it completely to create MTS.  The IBM/MIT team created the precursor to VM.  Also, the user-level code like compilers was reasonably movable between different OS (for instance my first paying programming job was in the CMU's IBM shop moving York/APL which was written for OS/360 to CMU's TSS).

Also, a lot of Amdahl customers ran MTS, not the basic IBM OS.  Also, at one point I was told by one of my former CMU co-workers who has moved to IBM to work on TSS, that there were more TSS customers on Amdahl equipment than IBM.  But IBM kept the TSS group alive for a long time.  [I'm not sure what the relationship was for support to be honest as I never lived it].

Note from my later LCC days, I was also under the impression that a lot of TSS sites were the ones that AIX/370 targeted to get them back into the IBM fold.   But it also took a lower-cost model of the 370 before that happened because they were targeting University types.

Finally, folks with Amdahl machines just looked at the PTFs and reimplemented them if they used an IBM specific trick (how they got them I'm not sure).   I do remember that it was not unusual for SHARE (the IBM user's group) to have Amdahl specific PTFs and often fixes/updates to the IBM code that came from folks rewriting them.  I don't know how that all worked.  I just got a stack of PTFs and had to deal with them, but I do remember some came from IBM some from SHARE and in the later seeing comments about running on Amdahl.