It's usually quite difficult to say for certain whether a job is eligible for a DBS (was the CRB) check (i.e. standard or enhanced) but in your case it seems pretty obvious - that job is almost certainly not one that will be eligible.
Couple of things to point out:
1. It could be that they state 'CRB' (for the reasons you mention) but actually mean 'basic disclosure' - this is something all employers are entitled to carry out, and is obtained from Disclosure Scotland
2. Is your conviction spent? You say a 'serious crime' - what was you sentenced to? This is important, because if it's spent, then it won't come back on a basic disclosure, so you wouldn't need to disclose, but if it's still unspent, you'll need to disclose if they're asking
3. If they try to do a DBS check on you, our advice would be to try and delicately question this, but then ultimately you'll have to consent to it (as you say, it's hard to challenge there and then) but then use the DBS eligibility query process
All of this is covered in a guide we have written on the DBS process - see hub.unlock.org.uk/knowledgebase/unlocking-criminal-record-checks-guide-people-criminal-record/
On balance, I suspect the employer has made a mistake in stating 'CRB' - they probably mean a basic disclosure, which then makes it important as to whether your conviction is spent or not. Even if it's unspent, it doesn't mean you can't take the job, it just means you'll have to disclose it.
Hopefully this helps put your situation into perspective. Take a look at the guide I've linked to above, and then if you have any further questions, please get in contact directly (our details below) - we'd be interested to know the outcome either way.
Unlock Helpline - confidential peer advice on overcoming the effects of criminal convictions
Call: 01634 247350 (Press 1)
Text: 07824 113848
Write: Helpline, Unlock, 35a High Street, Snodland, Kent, ME6 5AG
Find online self-information information, visit hub.unlock.org.uk
Need Unlocks advice? Visit our self-help information site
or contact our helpline