I apologize for my attitude and tone. I was speaking really in a general sense and not trying to direct anything personally toward you (although I know I used "you" language in that last post you quoted).
ilvl 719 is perfectly acceptable to join groups for Normal and Heroic HFC. I don't question that. But if you keep getting declined at that item level, then you have to ask yourself the question of: Why? Why am I getting declined at a 719 item level? Speaking if I was in your shoes:
Could it be because I still dont have my 4 piece set at ilvl 719? (because the mere having 4 piece gives most classes a 10-20k instant dps increase)
Could it be because the group I am applying to is looking for a higher item level?
Could it be because the group creator checked my armory and looked at my raid history on that toon and I little to no heroic HFC kills?
Could it be because I am not saying the right things in my note to be invited?
There are a number of reasons why a group leader wont accept players. The main of which is there are probably other people applying to the group whos item level are 10 levels higher than you. Again, if you were the raid leader, and 2 ret paladins applied to your run, and one was ilvl 719 and the other was 729, which would YOU choose? It doesn't matter if the 719 player has mythic 13/13 raid experience. What matters is, on first looking, only having ilvl to go off of, the likelihood of the 729 player performing better is higher than the 719 player.
So, how do you combat this? Look for groups whos requirements are lower. Create a group yourself and invite people of similar item level (although you would be more likely to invite any players whos item level was higher than your requirement). Join a social guild who casually raids and if they are starting a raid while you are on, ask to go.
The point is, the game has changed dramatically since the days of having to look in trade chat to find a group. There are so many other avenues of forming groups (not using the matchmaking queue) today than there was then. The implementation of CRZ, Cross Realm Servers, Battlegroups, Group Finder Tool... all of these together are powerful to allow players to form groups in relatively a small amount of time.
Even when im wanting to join a 5 man mythic dungeon in the group finder tool, i can get into runs within 5 minutes at a sub 700 ilvl. I just have to look for groups whos requirement is lower as well because I know groups that are looking for 720+ im not going to get into those.