What you call phrasal verbs have always been one of the messier parts of English syntax, and grammarians do not agree on what to call them, or how they are put together, or what to call their components.
Your first source is rather old-fashioned in one respect: it calls words like on and in ‘prepositions’ only when they take explicit objects; when they do not, it calls them ‘adverbs’. Other grammarians call on and in used in verb idioms like this ‘particles’ when they do not take objects; and still other grammarians, represented by your second source, claim that they are always ‘prepositions’, but may be used either transitively, when they take objects, or intransitively, when they don’t—just like transitive and intransitive verbs. This last version has the prestige of the highly admired Cambridge Grammar of the English Language (CGEL) behind it; but it is still contested.
Everybody, however, acknowledges that there are three different patterns, and my advice is that you focus on that. You will have to learn every single one of these idioms individually anyway, and will have to know which pattern each idiom follows. Don’t worry about what to call the pieces, just know how the pieces are used.
Short answer
to withdraw from a situation or to quit participating in a project or task, etc., and to thereby cause a negative consequence for someone.
Longer answer
We often use verbs (including phrasal verbs which this could be considered) followed by "on" to add a meaning something like "blamefully causing a negative consequence for someone or something."
For example, "She went crazy on me." Would generally mean that I was depending on her company or assistance with something, so her going crazy caused me some problem or distress.
To pull out means to depart (especially by vehicle, which I assume comes from carriages or coaches being pulled by horses, for example) or to withdraw:
pull out
- To leave or depart: The train pulls out at noon.
- To withdraw, as from a situation or commitment: After the crash, many Wall Street investors pulled out.
Since the first definition means a vehicle leaving, it would not normally be followed by on unless it meant on time or on a surface: The car pulled out on/onto the dusty road.
We can guess that it's more likely you ask about pull out on with respect to definition 2, because the three words seem to go together and in a way such that the meaning would be less obvious to many English learners.
So, to pull out on someone in this sense likely means to withdraw from a situation or to quit a project or task, etc., and to thereby cause a negative consequence for someone.
Examples:
She promised to invest $2 million in our company. We spent weeks preparing plans and drafting legal agreements in preparation for that. Then she pulled out on us at the last minute. We were so disappointed.
They were engaged for three years. Then John pulled out on her on the wedding day. He just left town without telling anyone.
He promised to help me move all of my things to my new apartment, but then he called and pulled out on me, saying he was too tired from work.
Best Answer
"Compensate with" is the instrumental form: someone is using something as a compensatory agent.
"Compensate for" refers to the shortcoming for which compensation is needed.
Your example, slightly rephrased: "Its high quality cannot compensate for its high price". Or "Its high price cannot be compensated [for] by its high quality". The "for" in the second form is more US than Commonwealth usage.