"Based on what evidence do you say that?"

Do you think it is okay to use "based on" at the beginning of a sentence? For example saying sentences like:

• Based on what empirical evidence do you say that?
• Based on what order did you put the songs on the album?
• Based on what information did you believe that I was lying?

My gut feeling says questions starting with "based on" might be wrong. Can they be used by native English speakers?

Convert them all into their respective answers:

• I say that (whatever "that" is) based on this empirical evidence: ...
• I put the songs on the album based on this order: ...
• I believed you were lying based on this information: ...

So they're all grammatically correct, but worded... strangely, especially the second one (it makes it seem like the order of songs on one album is based on the order of songs on another album).