So theres a few things to keep in mind here.
A diagnostic scan can consist of many different areas.. Strictly speaking Vauxhall equipment (which you local garage probably didnt have) would perform a more detailed scan for faults.
That said, its not always the case that there is a fault code to indicate where the problem lies. Fault codes can only be generated if the system at fault has an associated diagnostic monitor, many will not.
As for the immobilizer, this is one of the systems which does have some good monitoring.
If it is an immobilizer fault a repeated flashing symbol, car with a spanner across it or the MIL (yellow engine symbol), will indicate a fault..
Normal operation will be a brief flashing of the MIL and car/spanner light with the ignition on.
These things, the symbols, are, or rather should be, well known to the garage as to what to look out for in the case of a failed immobilizer.
In cases such as this the only thing to do is normal practice when engaging someone to perform a job.
Clear, itemized details on what they are doing or plan to do.
What they have done already and the outcome.
A clear definition of how much they charge per hour.
Defined points in time at which you both agree to as to how to proceed, for example, you might not want any replacement parts fitted without prior consent and knowledge as to how much it will cost and the reasons why they feel this will fix the issue.
No doubt you will come up against "I cant tell you how much this is going to cost..." which is a fair statement. But there is no reason why the above boundaries cant be established. What they can tell you is what they have already done (you might decide to remove the car and take it to another garage in which case giving the new garage details of whats been looked at is vital).
The reason many people get stuck with a large bill is they leave the garage to do what ever the want to with no contact with the customer as to what its going to cost. And many times the quickest things to try are numerous replacement items.
I always compare it to a builder coming to fix an unknown leak in the roof. You wouldnt let them start without knowing how much it will cost and whats involved in the repair, and is there any potential for unseen issues.
Just be clear with them that you want to be kept fully informed of their progress. This is a far better way to approach it as opposed to getting ideas on what to tell them which may help them fix the issue. It may well take time to do however in a two man garage if they have several cars, they cant dedicate one person for a whole day to look for a difficult fault, so this will inevitably take time but this should be reflected in the final itemized bill.
If you need any further information just get back to me..
All the best