Dave,
Here are relevant rules that provide some guidance.
25: Cards & Chips Kept Visible, Countable, & Manageable. Discretionary Color-Ups
A: Players, dealers, and the floor are entitled to a reasonable estimation of chip counts; thus, chips should be kept in countable stacks. The TDA recommends clean vertical stacks of 20 same denomination chips each as a standard. Higher denomination chips must be visible and identifiable at all times. If a floorperson cannot look at a chipstack and quickly estimate its value, players likely can’t either.
49: Accepted Action
Poker is a game of alert, continuous observation. It is the caller’s responsibility to determine the correct amount of an opponent’s bet before calling, regardless of what is stated by others. If a caller requests a count but receives incorrect information from a dealer or player, then pushes out that amount or declares call, the caller has accepted the full correct action & is subject to the correct wager or all-in amount. As with all situations, Rule 1 may apply at TD’s discretion. See also RP-12
54: Pot Size & Pot-Limit Bets
A: Players are entitled to a pot count in pot-limit only. Dealers will not count the pot in limit and no-limit.
60: Count of Opponent’s Chip Stack
Players, dealers, and the floor are entitled to a reasonable estimation of opponents’ chip stacks (Rule 25). A player may request a more precise count only if facing an all-in bet and it is his or her turn to act. The all-in player is not required to count; on request the dealer or floor will count it. Accepted action applies (Rule 49). Visible and countable chip stacks (Rule 25) greatly improve counting accuracy.
RP-12: Dealers Should Announce Bets & Raises
Dealers should routinely announce non-all-in bet values as betting proceeds around the table. All-in bets will be counted only on request of the player currently facing action. Accepted action continues to apply (Rule 49). Scheduled and discretionary color-ups improve bet countability.
According to Rule #25 and #60, the player is entitled to a reasonable estimation. Rule #60 says that when the player is also facing an all-in bet and it is their turn to act, they may request a more precise count. However, it pertains only to the all-in wager, not another player's stack who has yet to act. I'd rule that your player is entitled only to a reasonable estimation of that player's stack.
These rules regarding visible, countable or estimable chip stacks exist to promote orderly and timely game flow. Requesting full counts of stacks not all-in or pots in other than pot-limit games should not be honored. The errant requestor and players with disorderly stacks should be cautioned accordingly.