While you may feel that your military background means you have been following different procedures and standards to civil flying I would not make the same assumptions.
Civil training or should I say - Good Quality civil training will have very well defined standards for every stage of the PPL course (as well as all others). If you can not obtain a copy of a good training manual from such an organisation then I recomend that you research the AOPA publications that provide generic aspects of the course and a basis for a good document.
The first solo is the first time the student becomes the pilot in command and has sole responsibility for the safe execution of the flight as briefed. Once they taxi out, they are pilot in command and have sole responsibility for the safety of themsleves and their aircraft and anything they do is 100% their responsibility.
Training towards this starts on day 1 exercise 1 and is a gradual laid down and recorded process. The student records will contain reports of progress and if necessary lack of progress and certify that key standards have been acheived for each lesson leading up to first solo.
Therefore the decision to send the student solo is not one that is made as a snap decision or based on as some people say 3 good circuits. Such decisions are risky and can often be based on a temporary good period of operation that may not continue into the solo phase. They are also difficult to supervise and document adequately not to mention causing problems when restricted FI's provide the training prior to first solo.
Having demonstrated the required standard on all the relevant exercises from the sylabus, the instructor will determine that the student has reached the required standard for solo. This is the time at which the student can progress to exercise 14 - the first element of which is a dual check prior to the first solo. However, before they do, most organisations will have some form of certificate or checklist that both the student and the instructor signs to show that they both agree everything required to be done has been done.
Therefore, the standard required is in simple terms is to have satisfied the instructor(s) that if authorised in suitable conditions the student is capable of safely acting as pilot in command of the aircraft including being capable of coping with any unexpected emergency (eg engine failure) that may occur while they are pilot in command.
So we end up sitting next to a student that is recomended for first solo. perhaps this was done by yourself or perhaps it was another FI - perhaps a restricted FI. However, provided that everything has been completed correctly this student should be capable of
repeating the previously demonstrated standard which put them in this situation.
You have read the record, you know the conditions are suitable so you complete the pre-solo check. Now this may be 3 or 4 circuits because at this stage you are simply confirming that the previous standard is being
consistently maintained. If it is - they go solo.
Therefore I hope that I have described a standardised gradual process that reaches a point where the student has demonstrated the required standards of both knowledge and skill and the next element which is a further confirmation immediately prior to the solo exercise.
I recomend that you also talk to some experienced instructors from the UK Microlighting training organisations. Their sylabus leaves solo until the very end rather than the JAR sylabus which places it somewhere in the middle. You may get some intersting comments regarding the balancing of giving a boost in confidence to making sure they really can be PIC before going solo.
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Did I
up?
Were you PIC at the time? No. So provided you reasonable assessed the conditions as suitable and briefed correctly, the pilot in command of the aircraft at the time was 100% responsible. Students seem to loose sight of this - they are PIC and they are 100% responsible for everything that a PIC can be held responsible for - notams, weather, not breaking the aeroplane!! Insurance!!!!!!