They did sort out a similar situation in the 2013 ECF, but this Spurs team was really dominant. In hindsight, losing Mike Miller was probably a problem for them (despite Rashard making shots against us, Miller had the higher BB IQ). Battier and Allen both started to show their age too.
About luck, I just think Pat has made generally good decisions. He put the Heat on the map even before the big 3, with their championship in 2006. There might be some luck involved, but I actually think he's extremely competent in what he does.