Yea...you should get your eyes checked. I did not say there was anything wrong with the Bloomberg terminal. I used to work at a firm that had access to Bloomberg, if you look at the terminal closely, you will see that out of sequence trades are quite common. That was my only point regarding Bloomberg.
QuantQuote also offers Tick resolution data:
https://quantquote.com/products_tick-data.php
If you look at their Tick resolution data docs, you will see that they do NO FILTERING, and include every single trade, including out of sequence trades, along with their sale condition.
However, as I demonstrated in my earlier example, QuantQuote's methodology of removing late reported trades is the ONLY unbiased way to represent the data. Did you read the QuantQuote FAQ I linked to earlier? (https://quantquote.com/support_glossary.php#OFS)
QuantQuote is NOT changing the order of the data, they just don't use late reported trades when calculating low/high for a minute bar. That is the MOST accurate way to represent the data in a one minute bar format.
At the firm I used to work at, when reading off of live feeds, we also threw out trades with sale condition Z (out of sequence) for the exact reasons I brought up earlier so believe it or not, this is very common practice among truly professional quants.
Now, if you still have any doubts about the validity of this process, note that Tickdata (ridiculously expensive, but also well regarded) also performs this same type of filtering. Look at the second white paper here: http://www.tickdata.com/support/white-papers/