The manual shows two BT module to µC examples and one BT module to PC serial port example. Only the latter uses an inverter (i.e. their RS232 module).
The PIC UART will likely have a Schmidt Trigger input - 3.3V is too low to be seen as logic high - 0.8Vdd is required. With SerIn or SerIn2 and TTL inputs, logic high is 2V.
FIG 14 & FIG 15 of this app note http://www.zbasic.net/appNotes/AN213.pdf shows how to interface to the Schmidt Trigger input.
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