Atmega2560 USART UDR r/w conflict possible?
Is there any possible way that data written to the UDR register could somehow be read out again?


No, there is no possibility. The datasheet says:


  The USART Transmit Data Buffer Register and USART Receive Data Buffer Registers share the same I/O address
  referred to as USART Data Register or UDRn. The Transmit Data Buffer Register (TXB) will be the destination for
  data written to the UDRn Register location. Reading the UDRn Register location will return the contents of the
  Receive Data Buffer Register (RXB).


Further on it says:


  The transmit buffer can only be written when the UDREn Flag in the UCSRnA Register is set. Data written to UDRn
  when the UDREn Flag is not set, will be ignored by the USART Transmitter. When data is written to the transmit
  buffer, and the Transmitter is enabled, the Transmitter will load the data into the Transmit Shift Register when the
  Shift Register is empty. Then the data will be serially transmitted on the TxDn pin.


And for reception it says:


  The receive buffer consists of a two level FIFO. The FIFO will change its state whenever the receive buffer is
  accessed. Due to this behavior of the receive buffer, do not use Read-Modify-Write instructions (SBI and CBI) on
  this location. Be careful when using bit test instructions (SBIC and SBIS), since these also will change the state of
  the FIFO.


So the only thing it is possible to read is data that has been received via the RX pin (and then once and once only). All written data (assuming there is room in the TX buffer) is sent out of the TX pin.

If you are getting TX data appearing in the RX buffer then somewhere there must be some kind of connection between the TX and RX pins - either in software at the remote end (the remote device echoing everything it receives, which is perfectly possible depending on what the remote device is), or though a fault in the cabling or circuit design.