Whether black tank drain valve is open or not has no bearing on whether water can flow thru flush system
Having the dump valve open while using the flush system is 'JUST In CASE' preventative measure....get distracted and water continues to flow in until tank is FULL the OVER FULL ----blowing past toilet bowl seal OR worst Blowing out tank vent on top of RV
The hose connection MAY have a check valve inside it....like the city water connection.
Most don't so water can flow back out after disconnecting hose
The other 'check valve' is actually installed high up typically inside the bathroom cabinet or even a closet.
It is an 'anti-siphon vacuum breaker' on the inlet line.
Some times that can fail...usually you will have water flowing out of open top when that happens.
More typical when there is not flow (and as worked OK in past) is the nozzle in tank has become clogged.
Some nozzles can be removed and the holes in nozzle cleaned....depends on installation used,
*Nozzle glued in place
*Nozzle held in place with screws
*Nozzle spun welded in place (spun at high speed creating heat that melts tank wall & nozzle flange together)
Anti-siphon Vacuum Breaker
Several versions.....Black/Cheap junk to Brass/better quality
Is it time for your medication or mine?
2007 DODGE 3500 QC SRW 5.9L CTD In-Bed 'quiet gen'
2007 HitchHiker II 32.5 UKTG 2000W Xantex Inverter
US NAVY------USS Decatur DDG31