Jesus said, "I am the way, the truth, and the life", John 14:6. So talking "the truth", possibly, might be, talking about Jesus.
"speaking truthfully" may or may not mean the same as "speak the truth".
What does "aletheian" mean in Eph 4:25?
There are a number of verbal components/ideas in Ephesians 4:25.
- The first, ⲁⲡⲟⲑⲉⲙⲉⲛⲟⲓ,is a participle describing how they are to carry out the main verb. They are to have a manner of "setting aside that which is false."
- The main verb, ⲗⲁⲗⲉⲓⲧⲉ, tells them what they are to do. They are to speak the truth.
- The final verb in the verse gives the reason why they are to do this (ⲟⲧⲓ): They are members of one body.
So, notice that the manner of "setting aside everything that is false" would also include setting aside true statements that mislead the hearer. Likewise, notice the motivation: if we are one body, why would one member of the body hurt another body part? Omitting key truths for the sake of deception would be doing just that.
Finally, in the greater context, a few verses earlier, Paul invites them to "speak the truth in love" (“ἀληθεύοντες δὲ ἐν ἀγάπῃ” (Ἐφεσίους 4·15 THGNT-T)). Notice how this makes the same point in different words: we speak the truth. But the manner & motivation in our hearts is ⲁⲅⲁⲡⲏ love: that which seeks the best for the other person.