Getting married in the US, flying straight back afterwards

So I'm flying over to the US in 3 weeks (over there for a week), getting married, and we'll be leaving the US the next day. My fiancée has been living in the UK for nearly 2 years now, on a student and then post-study-work visa, so she's fine.

However, given the thoroughly unwelcoming experience I've had with immigration at Newark (last time after saying I was visiting my fiancée's family I was redirected to a waiting room for half an hour or so while the staff played with their phones and read magazines before deigning to check their computers to find that - shock, horror - I actually had a flight back booked) both my fiancée and in-laws are convinced that if I say I'm getting married they won't let me in. Accordingly, they're trying to persuade me to say that I'm on holiday (reasonable enough) plus a business trip (true also - a potential supplier is about 3 hours from her house, so I'm hoping to visit them while I'm over.

To me, however, this sounds like a very dodgy plan - much more likely to cause trouble in future than save it now. Has anyone else been in this situation? What documentation did you bring with you to persuade them that you were really going home again? I've read the US Embassy London website in the past - currently can't find the link - which basically says that ESTA is fine and you just need a return ticket. Is this good advice? Would showing them my MOD 90 (British Army ID Card) help? (bit reluctant to do that as I'd feel a bit of a Walter Mitty!)

All in all, thoroughly confused!

Whatever you do, do not lie to or omit the truth from US immigration - tell the truth about why you are there if they ask you. If you lie (i.e. say you are on a business trip) and then get caught in the lie you could be banned from entering the US altogether!

It is perfectly fine and legal to marry in the US as a visitor. It even says so on the US Embassy in London website, where tells you that if you are not planning to live in the US, you should enter as a visitor to get married:

Fiance(e) Visas

If you will marry in the United States with the intention of taking up  indefinite residence after marriage, you will require a fiancé(e) visa.  For further information, please follow this link.

Note:  If you will do not intend taking up indefinite residence in the United States but will continue to live and work abroad after the marriage ceremony you should apply for a B-2 visa, or if eligible travel visa free under the Visa Waiver Program.

(emphasis mine)

See: http://london.usembassy.gov/immigrant-visas/marriage-to-a-u.s.-citizen.html

You can always print out that page to show to the immigration officer at the airport.

It might be a Newark thing as I had trouble at Newark last year when I entered on a B2 visitor visa (I am no longer eligible to use the VWP so I applied for a visa in advance) - I was put in the back room and questioned for several minutes on my intentions in the US and whether or not I was still a student in the US - it was my third US visa (I was only staying for 2 weeks en route to travelling around South America). When I came back to the US via Miami though 8 weeks later, I was let in within 2 minutes, with no problems at all!

My DF always comes here thru EWR.  He's never had to sit in the little room, but the last guy (his 4th time seeing me in the US) the IO asked where we met and when he was leaving.  DF (just as when I go to the UK) brings a letter from his boss stating that he's coming  back.  For the wedding, he'll have a printout of the link provided above as well.