Issues over lower league structures
Pickering and WRU chief executive Steve Lewis took a presentation - known as the "Red Zone Roadshow" - around Wales to answer criticisms, but unrest has continued.
"The clubs have a right to call an EGM and they've done that," Pickering told BBC Wales.
The WRU did not replace former boss David Moffett
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"Only 10 out of our 245 member clubs need to agree in order to request an EGM, and we've made ourselves unpopular in some areas by making tough decisions over the last couple of years.
"I don't believe that the EGM is about Mike Ruddock's departure, people have largely accepted that and we've moved on.
"The core issue is the governance of the Union."
A WRU board meeting will be held next Thursday to discuss the EGM request.
The WRU management say that - if it is to be held - the EGM must take place within 28 days of it being called.
But the clubs claim the Union has to hold the EGM and that it must take place within 21 days of the request being lodged (in this case 31 March).
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THE 'REBEL' CLUBS
Bridgend
Morriston
Trinant
RTB Ebbw Vale
Blaina
Newbridge
Bonymaen
Pontycwmmer
Pontardawe
Resolvent
Cwmgrach
Usk
Chepstow
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The Union has been advised by former board member Howard Watkins that he is representing the 13 clubs making the request.
The ongoing political manoeuvrings could have a key impact on who becomes the next national coach.
The current Union management are thought to be keen to appoint Leeds director of rugby Phil Davies.
But Scarlets supremo Gareth Jenkins would seem to be the peoples' choice, and he says he would relish the job if the current Union management was to be replaced.