I was told by a Texas real estate agent that if I used an FHA loan to purchase a duplex, triplex, or 4-plex that I intended to occupy that I could not collect any rent money from other units because that wold be considered mortgage fraud because FHA loan can not be used for investments. 

agree with @Andrew Syrios  this is a poor scheme fraud with default and economic danger to the owner of the property...

@Tiago Martins IF I understand correctly, you're proposal is to lie to the lender in order to get the loan.That seems like the textbook definition of mortgage fraud.

If a buyer is having a hard time getting a loan for a townhouse that a friend wants to sell for $51k, because the bank requires the loan to be at least $50k after 15-20% down, would it be okay for his friend (the sel...

They likely do not as a mortgage product that did, would have a higher rate pricing adjustment than what he is quoting you, so he is likely inadvertently going to cause you to commit mortgage fraud...or is as typical with Quicken, a couple weeks into the process they will say oops, we need to put you into a different loan product.Definitely get a different lender quote from the first guy, as it does seem to be on the high side, but dont go with one of the worst known lenders in the country. 

Fraud or just a line of business that did not work out for Cap One.

I have never had this issue before without it being clear cut deed fraud.

@Justen Ashcraft Even if closing times are identical and there is zero chance of an appraisal issue, a cash offer is still better.  

By your own admission this is what is called FRAUD BY INDUCEMENT.Typical for FRAUDS AND SCAMMERS!

I wouldn't recommend using them:https://www.biggerpockets.com/forums/52/topics/499696-beware-of-fraud-by-erentpaymentcomhttps://www.biggerpockets.com/forums/81/topics/498197-having-trouble-with-the-site-erentpayment