I'm looking to buy an STP to Bedford super off peak day return for Sunday from the Trainsplit site. I'm offered a London Thameslink to Bedford ticket for £11.25 ( Network card discount ) but the itinerary suggests that I take an EMR train. Will the said ticket be valid on EMR trains or will I have to use Thameslink ?
Yes; London Thameslink is just the origin of the ticket, a station group that incorporates all the stations along the Thameslink 'core' from Elephant & Castle and London Bridge up to St Pancras.
As the route is 'any permitted' it's valid on all operators that run services along the permitted routes. And therefore valid on EMR.
It's worth noting that as a matter of consumer and contract law, you are always entitled to travel in accordance with the itinerary you're offered when buying your ticket - so even if this had been a mistake, you would still be allowed to travel as shown.