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White prints on the Time & Sales means that a trade happened in between the bid and the ask. How is that even possible? The only two answers that come to my mind are.
There was a hidden order in between the bid and the ask which got executed.
The software showing the Time and Sales didn't have the time to show a higher bid or a lower ask because the trade happened so fast.
Your two scenarios make sense. You didn't specify the security so I'll toss a third one out which applies to options.
I'm looking to roll a somewhat deep ITM long put down a strike for a credit of $4. The B/A spread on each side is quite wide so I place a vertical spread order for the roll, splitting the B/A on each leg. I don't care what the fill price is for each leg as long as I get my $4 credit. Once in awhile, one or more spread has legs that are filled are well away from the current B/A.
For example, all but one spread are filled at $3 for the buy and $7 for the sell, netting me my $4. The outlier spread is filled at $3.50 for the buy and $7.50 for the sell, again netting me my $4. No advantage or disadvantage to me. However, my fill prices on the outlier are well outside the current B/A spread. This could occur just as well between the B/A spread that you noticed (no Time and Sales quote but it trades there).
My guess is that there's a call buyer or call seller at one of my strikes who either split the B/A poorly or didn't split it at all. The market maker doesn't want that risk so he combines the 3rd party's call with one of my puts in a conversion or a reversal and then fills my other leg $4 away. IOW, he's splitting the B/A for me (capturing half the B/A of my puts) and capturing the bulk or all of the call's B/A spread from the 3rd party.
In Australia we have a system that allows trades to be executed between the bid and ask, I think they call them centerpoint trades. It allows the non retail investors a small advantage in trading over the retail traders. Some may say that is unethical or illegal, but because it requires a willing seller and buyer at that price then one could argue that it really is no different to an off market trade, where two will participants trade exclusively at an agreed price, which is legal and ethical
Thereis a third answer: your bid/ask are not what you think they are.
Particularly in stocks in the USA (but also i.e. canada) there are quite a lot of exchanges all with their own order books. There is one consolidated order book.But there is a possibility that some exchanges have a little different pricing for some time.
i.e. look up https://www.investopedia.com/terms/l/lockedmarket.asp - decribing a similar scenario.
So, it is possible that your bid/ask is from one exchange or the consolidated (fake and a little lagging) book while the trades are per definition from a specific exchange an may have a slightly different bid/ask.
Keep in mind that many times what you're seeing are the BEST bid and BEST ask prices, but there can be many others as well, some of them well outside the range of the rest. Every market maker sets their own bid/ask prices, depending on how competitive they want to be on a particular issue. Widely-held stocks can have hundreds of market makers, each with their own bid/ask prices.
Also, parties can agree to trades at ANY price, whether they're public or not.
Finally, some trade volume you see comes from market makers trading for their own books.
The point is, there are MANY reasons why you'll see what you're describing, but it isn't necessarily anything sinister or illegal.
