Re: Offering Asr prayer as Qaza
From my understanding, one can pray Qaza whenever one wants to (except time when one should avoid Salah). That means, one can pray Qaza of Asr during Maghrib time, before or after Maghrib Salah.
Anyhow, if situation is that praying Qaza would make one miss Maghrib or miss Maghrib Jamaat, than praying Maghrib would have precedence over Qaza.
Else, there is no precedence in order of performing Salah (be they Sunnah, Nafil or Qiza), other than that one should do his best to perform farz salah on time.
As for not praying Qaza of Asr, I believe you may have read in book that if one have to pray Qaza of Asr then they should not pray Qaza after end of Asr time (makruh time). Probably writer of the book may have mentioned that in such way that it caused confusion.
Thus, right thing to say is that, one should not pray Asr Qaza at time just after end of Asr time and just before start of Maghrib time (as time between these two times is Makruh time for Salah … and one should avoid Salah during Makruh time), but it does not mean Qaza of Asr cannot or should not be prayed at any other time.
Actually, even though not preferred still current Asr prayer can be prayed during this Makruh time too, if Asr of that day got delayed for some valid reason.