It helps to post the text of the cards when you have a question.
False Echo wrote:
Whenever you pass a piece of unrezzed ice, you may trash False Echo. If you do, the Corp must rez that ice or add it to HQ.
Cyber Threat wrote:
Play only as your first [Click].
Choose a server. The Corp can rez a piece of ice protecting that server. If he or she does not, make a run on that server, during which the Corp cannot rez ice.
Nothing on False Echo mentions modifying the circumstances of the corp rezzing the ice. It merely states that the corp has to rez that ice or add it HQ. If another effect prevents them from rezzing that ice, like cyber threat or a lack of credits, then the Corp can't rez the ice and it must be added to HQ.
In a situation where a card does specifically allow something that another card forbids, the keyword "Cannot" typically takes precedence.