Power Grid removing lowest plant if first player passes
No, this is no part of the original ruleset; the base-game rule has never changed and remains as you quoted: if nobody buys a Power Plant, then at the end of Phase 2 you discard the lowest Power Plant and draw a replacement. Source: it simply doesn't exist.

On the contrary, your friend's house rule is imbalanced; discard the lowest one only if the first player passes? This really tilts the balance in favor of the other players. Not to mention that it completely breaks 2-player games by disincentivizing players from getting the pole position.



edit: Please note that this is the base game rule: all players have to pass to remove the lowest power plant. The Russia map from Power Grid: Russia &amp; Japan (2010) amends this base-game rule (source, p. 2)


  Starting in game turn 2: when the first player in a game turn does not
  offer a new power plant for auction and instead passes, remove the
  smallest power plant in the actual market and replace it with a new
  power plant from the stack. This rule replaces the base game rule, so
  that players DO NOT remove the smallest power plant from the
  market when all players pass and nobody buys a new power plant.


Emphasizing: please note that this is an amended rule on a specific expansion map (Russia). Otherwise, the rule is as stated: all players have to pass.