The confusion arises from the mixing of two issues:
 
(a) Following another madhhab  completely in a complete action, and 
(b) mixing the positions of more  than one madhhab within one action, in such a way that it is not  independently valid in either one (talfiq). 
The latter is impermissible  and invalid according to the fuqaha. Ibn Abidin (imam of the late Hanafi  school for fatwa) and Ibn Hajar al-Haytami (imam of the late Shafi`i  school for fatwa) both transmit scholarly consensus (ijma`) regarding  its impermissibility.
 
Following another madhhab completely in a  complete action, however, is valid according to the majority of the  scholars of usul al-fiqh, and fuqaha, on the condition that there not be  a systematic seeking out of dispensations. This was confirmed by Ibn  Abidin in his Hashiya, Tahtawi in his Hashiyat al-Durr, Abd al-Ghani  al-Nabulsi in his Sharh al-Tariqa al-Muhammadiyya and in his treatise on  ijtihad, taqlid and talfiq, and is the position adopted by the Syrian  Hanafi scholars.
 
The scholars of the Indian Sub-continent  generally do not allow this, except under exceptional circumstances, but  not because it is per se invalid, but for obvious reasons:
 
(a) In their millieu, it is not normally possible for one to find a qualified source or scholar from another school; 
(b) To close the door to the systematic seeking of dispensations. 
But,  even Indo-Pak scholars who advocate this position admit, this is more  an answer of prudence than a theoretical impermissibility. 
I  wonder whether the position enunciated in the major texts of the school  is not more suited to our situation in the West. People have a lot of  difficult situations and challenges in their lives, and this makes  things easy for them while remaining within the boundaries of sound  sunni scholarship.
Sticking to One School
It  is not religiously binding on the Muslim to stick to one school on all  matters, without exception, as both al-Tahtawi and Ibn Abidin (Allah  have mercy on them), the two leading late authorities for fatwa in the  Hanafi school, both explain. Rather, there is nothing wrong with taking a  dispensation if there is a need; what is impermissible is to make it a  habit to seek out dispensations [i.e. even if there is no hardship or  need]. 
The Path of Taqwa 
The path of  taqwa, as the scholars explain, is to avoid taking  dispensations unless there is genuine hardship in following one's own  school. In fact, they say that those who have learned their own school  should seek out the strictest positions from other school whenever  reasonably possible, so that one's worship and practice is sound without  argument.
 
May Allah grant us beneficial knowledge, and the  success to act according to it, on the footsteps of the His Beloved  (Allah bless him and give him peace), with the secret of sincerity,  without which actions are but lifeless forms. 
And Allah knows best. 
Wassalam,