I got caught between the two once. Came out of the Underground and wanted a Priv ticket to Lewisham, which is cheaper than anything available from the TVM. Lewisham ticket office also would have been closed by the time I reached there. Southeastern said I'd have to buy a ticket from the TVM and travel to Charing Cross to have it refunded and sold a Priv ticket. The other options were to be let through, where the RPI present would charge me "big fine", or implore Underground staff to let me back in without a valid ticket, go out the other end and go to a different station to buy a Priv ticket - LU can't sell Priv tickets to holders of non-safeguarded Privs. National Rail and the TSA state Waterloo East has no ticket office, but Southeastern are adamant that a separate station with a ticket office counts as a ticket office for Waterloo East.
It's stupid to have a situation where you can be stuck between gatelines with no means of leaving the situation - staff who are unwilling to excise common sense when the ticket issuing facilities are inadequate and no warning of the limited facilities available. Sometimes the Underground advertises that certain exits can only be used by ticket holders, but that isn't even the case because there are LU and Southeastern TVMs in place.