It might work with rs.Fields("myFieldName") = .txtMyTextBox but I'd never not use Me as a qualifier, so
rs.Fields("myfieldName") = Me.txtMyTextbox
You have the additional circumstance where one is bound but the other (the one with the expression in the control source) is not. In any event, I'm surprised that either of the first 2 worked at all if that's how it was really written.
The more we hear silence, the more we begin to think about our value in this universe.
Paraphrase of Professor Brian Cox.