Illogical? Shirley, you jest. :) The proclamation is actually a few verses later and the Bible is clear:
1 Tim 2:5 : For there is one God and one mediator between God and men, the man Christ Jesus, ...
What else is there to say? I know you believe in ONE God. This verse leaves zero room for interpretation or inclusion of anyone else as mediator. This verse clarifies your verse. Yours talks about living people praying for one another, which is all well and good. Verse 5 leaves no mistake that there is only one go-between.
The passage (1 Timothy 2:1-5) calls for intercession done by Timothy (for example) for the king (for example) to Christ, Who is the sole mediator to God the Father. The "sole mediator", therefore, does not prohibit mediation of Timothy to Christ, but if so, then also by Mary or any other saint to Christ.