All they need on their website are simple straight foward words. WARNING - You can't come to the UK and use our same day processing service. You MUST apply online and STAY in your home country. Don' quit your job. Don't sell your things until you have our visa approved and sent back to you. My british husband read all the things I did and was in agreement with what I was doing.
I have student loans and car payments to make and this really was a curve ball that could have been avoided if it just simply and clearly communicated these things. If nothing else, I pray that my experience could help someone else from experiencing what I did. because it really is unnecessary and didn't add any value to my life. 
But what people are saying here is that the website clearly does state that you can't do it - in the eligibility section for the visa. Yes, okay, perhaps they could make it clearer, but it's definitely there.
If you go to the page for applying for a spousal visa to join your family member in the UK, you will see the following:
Apply to join family living permanently in the UK 
.
.
.
If you’re already in the UK
You can’t apply for a ‘family of a settled person’ visa - you must apply to remain in the UK with family instead.
So, then you go to the link for applying to remain in the UK with your family, and under 'eligibility', it says:
3. Eligibility
.
.
.
You can apply to extend or switch in any of these routes if you’re eligible, except if you have permission to be in the UK:
-    as a visitor
-    for less than 6 months – unless you got your visa to get married or become civil partners or you got your visa to wait for the outcome of a family court or divorce
-    on temporary admission or release (you don’t have a visa) – unless you apply in a 10-year route
If you had still been living in the UK on a valid student visa, then of course you could have used the one-day service and applied to switch to the spousal visa (FLR(M)); but as a visitor, it is not possible to switch because you don't have permission to live in the UK - your visitor visa only gives you permission to visit temporarily as a tourist, not live in the UK. 
I guess perhaps UKVI assume that no one would think to try to apply for an in-country spousal visa as a visitor, because in order to be allowed into the UK as a visitor to start with, you have to show you have no intention of living in the UK and that you have a life, a home and a job to go back to in your home country.
Which is the whole reason you were held up at immigration in the first place, because in order to qualify to enter the UK as a visitor, you have to show the following:
- a return ticket
- enough money to support yourself without working for the entirety of your trip
- that you will leave the UK within 6 months and won't try to live in the UK, which you show by:
1) having a job to return to (letter from your employer stating you have been given time off and the date you will return to work)
2) having a home to return to (evidence of a current tenancy agreement or evidence of homeownership)
3) having other ties you must return to the US for, such as family members to care for, appointments or engagements to attend etc.
_________________________________________________
 __________
For the record, US immigration is just as bad. The US immigration officers are notorious for being rude and and very abrupt. One time, my dad hadn't filled out his landing card correctly (he forgot to sign the bottom), and the US immigration officer practically threw it in his face and shouted at him to get to the back of the line (which was 2 hours long) and fill it out correctly - he wasn't even allowed to sign it at the desk.
In 2003, I moved to the US on a student visa, but I accidentally packed my visa documentation in my suitcase instead of in my hand luggage. When I told the immigration officer this, I was immediately escorted to a detention room and held there for 2 hours. 
I was in a room full of other detainees and when one young kid (maybe 13 or 14 years old) asked to use the bathroom, he was directed down the corridor. He came back a moment later to say he couldn't find the bathroom and the immigration officer shouted at him and told him to sit down and hold it. She flat out refused to show him where it was.
Eventually, I was collected from the detention room and escorted down to baggage claim to retrieve the documents, then I had to join the immigration line again to actually be allowed into the country. In all, it took me about 4 hours to get through immigration and I missed my connecting flight. Not a good start to my year living in the US and I refused to fly through that airport again for the next 10 years!