I think that "discretion" is usually reserved for when someone commits an offense that isn't one in the UK, such as countries where homosexuality is a crime. That clause exists to allow for cases like that, but with you don't expect a DWI to be subject to that discretion (since drinking and driving is illegal in the UK as well as the US).
Yeah, exactly. If it's a simple DWI, I don't think there's going to be any discretion used... it'll be a straight refusal.
The official guidance on this states:
RFL10.3 When can I refuse on the basis of non-custodial sentences?
Paragraph 320 (18A) and S-EC.2.5.(a) in Appendix FM of the Immigration Rules provides for a discretionary refusal of entry clearance where a person has been convicted of or admitted an offence for which they have received a non-custodial sentence or other out of court disposal that is recorded on their criminal record within the preceding 12 months of submitting their application. Examples of non-custodial sentences may include fines, Cautions, Warnings and Reprimands or suspended sentences.
I have a DWI/DUI myself. It's not a trivial thing at all... and it can have a big impact on immigration and visa eligibility. It happened in the UK (I'm a UK citizen) just before I was due to apply for a student visa for the US, and I had a massive panic that the visa would be refused and that I had just ruined my future career (thankfully I discovered they couldn't refuse the visa unless I was either an alcoholic or a danger to society).
Having the DUI on my record means that I am banned from entering Canada for 5 years from the end of the sentence - because it's considered a felony there. After 5 years (which was 2013), I can apply for rehabilitation to enter, but it costs over $200 and takes about a year to be processed. Alternatively, once 10 years have passed, I can travel to Canada without a visa (however, I believe I'm only allowed to do that once and then I have to get a visa).
I also have to apply for visitor visas to enter the US, because I was told by the US Embassy that any arrest, even if you were not convicted, makes you ineligible to travel without a visa (whether that's actually true or not, is debatable, based on the ESTA questions, but I've erred on the side of caution). I also believe I will need to apply for a visa if I want to enter Australia as well, as they take convictions pretty seriously too.