There is no question, a period of time spent on-call is not considered rest. It is considered duty time. 121 or 135, it makes no difference. Rest is rest and duty is duty, according to the FAA. Even pilots operating under 91 can be violated for flying without sufficient rest. Operate a flight without sufficient rest, whether other guys do it or not, and you may well find yourself with an expensive legal bill and no job prospects.

It's all been discussed in detail, with links to many relevant and binding legal documents, in these threads:
On-Call is not Rest
On Call vs On Duty

The "available" issue is directly addressed in this post:
Duty to Report vs Available