I came to play

[Hogtrail]

I Came To Play!
Pre-match Event
Cannot be blanked.
Your cards with "trash talk" in the title or text do not take up a Pre-match slot in your Ring.
When you would discard cards for your opponent's effects, you may instead overturn the same number of cards.
F: 0     D: 0     Permanent     Unique

Welcome to Monday Nitro!
Pre-match Event
Requirement: Allegiance: WCW
When you are a WCW Superstar, this card does not take up a Pre-match slot in your Ring, and when you Activate Where the Big Boys Play, you may put the cards on the bottom of your Arsenal instead.
When Houston, Texas is not in your Ring, you and your opponent draw 4 cards, and he randomly discards cards until he discards a hybrid card; then, you discard the same number of cards.  When Flanked by Arena Security is not in any player's Ring, all players' Starting Hand Size are -2, and all players draw 3 less cards for The Best Laid Plans.
F: 0     D: 0     Unique     Permanent     RMS logo     WCW logo

How do the bolded sections interact with each other?

[CreedP]

You, as Miz, have 7 cards in hand.
I have 5, so you have to discard.

You would discard a card, but you choose to burn instead.  You haven't discarded a hybrid card, so you have to keep discarding.

 - - -

Alternately, I'm the Miz, you have 5 cards in hand after discarding a hybrid.
I have 7, so I have to discard.

Instead, I overturn cards.

I still have 7 cards in hand, so I have to discard. 

CREED

[Ekhari]

So if the first case is your opponent plays Nitro, you could essentially overturn your entire Arsenal since you won't be able to "Discard a Hybrid Card" since you're overturning.

Would the second case work that way though?  If you play Nitro and therefore have to discard the same number of cards as your opponent did, you created the discard effect, not him.

[Hogtrail]

You, as Miz, have 7 cards in hand.
I have 5, so you have to discard.

You would discard a card, but you choose to burn instead.  You haven't discarded a hybrid card, so you have to keep discarding.

 - - -

Alternately, I'm the Miz, you have 5 cards in hand after discarding a hybrid.
I have 7, so I have to discard.

Instead, I overturn cards.

I still have 7 cards in hand, so I have to discard. 

CREED

So, basically, Miz cant avoid this discard?

I wasnt sure if it would be similar to E&C's Ability where he would reveal until he hit a hybrid, and then he would overturn that many

[Daeva]

Miz can't avoid this discard. The "discard until" template doesn't work well with replacement effects. Miz can overturn as many cards as he likes before he actually discards cards, though.

Ekhari is also correct that I Came To Play! doesn't work on your own stuff, so if he played Monday Nitro!, he wouldn't be able to replace the discard with an overturn. (Note also that the effect that makes the Nitro player discard is not a "discard until" effect, so things that replace discards will work like you'd expect them to.)