Yes, I believe that the obverse dies were kept more secure, because it was the image of the Emperor. This is the concept of the veneration of the image of the Emperor, of which a lot has been written. If an Emperor was declared damnatio memoriae, then his images might be destroyed, like statues and even coins defaced, though the defacing of coins seems to have died out by the 4th century.
An obverse die match to an official issue would make it very likely that a coin was also official. Many coins, however, look close and die matches in some circumstances, like slightly worn or a bit off-struck, might be hard to verify. Couple this with the fact that the person that engraved the official die might also be engraving unofficial dies. We know this happened because of a law recorded in the Theodosian Code-
Theodosian Code 9:21:2
Since some imperial minters are secretly and criminally engaged in the coinage of counterfeit money, all shall know that the necessity is incumbent on them of seeking out such men, that they may be tracked down and delivered to the courts, so that they may forthwith betray the accomplices of their deeds through torture and thereupon be sentenced to suitable punishments. (20 November 321)
counterfeiting was a huge problem during this period...here are two more laws issued a few years later.
9:21:3
If any person should mold a coin by false casting, We command that all his property shall be confiscated to the fisc and that he shall be punished with statutory severity, in order that such zeal for coining money may prevail only in Our mints. (6 July 326)
9:21:4
It was formerly established as law that, if money should be secretly stamped and coined on a farm or at a house without the knowledge of the owner, the fisc should vindicate to its own ownership the seat of the crime. Now it is our pleasure that a distinction shall be made, namely that if the owner dwells…at a very long distance from the said house or landholding, he shall sustain no loss. (4 May 326)
