Utter hogwash. Not only have I heard many, many people speaking Romanian in public in Pridnestrovie, I’ve also done it myself.
At least one-third of the people who live in Pridnestrovie speak the language, so I don’t know where this rumor came from, but it is a rather persistent one.
However, during the late 1990s right after the war, tensions were quite high. I have heard of stories of some (extremely minor) harassment of Romanian speakers during this time, but that’s all long in the past.
For goodness’ sakes, the government of Pridnestrovie organizes and finances folklore groups that sing traditional Moldovan songs. State-run television also runs Romanian-language news every single day.
And while there might be some differences in terms of how the language is written (Cyrillic vs. the Latin alphabet), when it’s spoken aloud, no one can tell the difference between Romanian and “Moldovan.”
Long story short? Anyone who tells you that you can’t speak Romanian in public in the Pridnestrovie is either lying or working for an EU/US-funded organization.