It depends on how big the bonus is.
I mean, if you get +20 to pathfinder lore, then yea. It locks everyone out that doesn't have it.
If you get +2 to pathfinder lore, then anyone can still attmept it. You can have a huge list that each gives +2.
And, according to the other source, there's only untrained/trained/expert. So my guess is +0/+2/+5.
P2 is going to add level (!) to all d20 rolls.
For training, your numbers +0, +2, +5 looks appealing to me.
What I would like to see is only four skills on the character sheet (and on the monster stat block).
Pick four skills that the character is especially known for. Pick which skill gets +5 − the one that most represents the character concept − and which three other skills get +2. All other skills are untrained.
So a glance at the four skills on the sheet, gives a good idea about what the character is about.
In terms of numbers: d20 + level + ability + training
A level 10 character with the relevant ability at +3 has:
Expert: d20 + 10 + 3 + 5 = d20 + 18
Trained: d20 + 10 + 3 + 2 = d20 + 15
Untrained: d20 + 10 + 3 + 0 = d20 + 13
The 18 is special. The difference between 15 and 13, means any character has a chance of succeeding in any skill.
Reducing the skill list to the four favorites, expresses the flavor of the character, emphasizes what the character is especially good at thus encourages teamwork, allows players to think creatively and optimistically in all skill checks beyond these four.