Can foreign banks provide money transmitter coverage inside the US?

No.

Please do not be fooled or conned by someone claiming to provide you with such an arrangement. Almost every licensed bank knows of this and many licensed non-banking financial institutions are also aware that their license cover does not extend out to the United States.

FinCEN actually has an advisory on this, and it is FIN-2012-A001, Issued Date: February 15, 2012, Subject: Foreign-Located Money Services Businesses.

In particular, businesses engaged in money transfers, who are physically outside the United States and pick up customers within the United States will be treated by the US Government as no different than an entity that is present inside the United States

Reference: FinCEN Advisory - FIN-2012-A001

So, licensed financial institutions like banks, money services businesses, money transfer operator, etc. are NOT covered by their license alone. They need to have a money transmitter license in the United States for each US state they would be working with customers in. Either that or they need to demonstrate a relationship with someone who is already registered/licensed inside of the United States who would be providing regulatory coverage for MTLs as part and parcel of the agreement with this foreign bank/MSB/MTL.

The rules are crystal clear on this. There is no grey area or ambiguity. An externally licensed institution cannot be a provider of money transmission in the United States without having licenses in the US or have an association with some entity that has the necessary Money Transmitter Licenses and is extending the coverage to you.

Also read: Do I need to have a US Money Transmitter license in order to sign a US customer up if my business is physically located outside the US?